BLVM 
ENTH 

SAL* 


RIS 


UNIVERSITY  OF  CALIFORNIA 

LOS  ANGELES 


AUG  2  7  1991 

ENGINEERING  & 

MATHEMATICAL 

SCIENCES  LIBRARY 


STAIR-BUILDING  AND  THE 
STEEL  SQUARE 


A  MANUAL  OF  PRACTICAL  INSTRUCTION  IN  THE  ART  OF  STAIR- 
BUILDING  AND  HAND-RAILING,  AND  THE  MANIFOLD 
USES  OF  THE  STEEL  SQUARE 


PART  I— STAIR-BUILDING 
By  FRED  T.  HODGSON 

IUTHOB  or  "MODERN  CARPENTRY,"  "ARCHITECTURAL  DRAWING,  SELF-TAUGHT,"  ETC. 

MEMBER    OF    ONTARIO    ASSOCIATION    OF    ARCHITECTS 


MORRIS  WILLIAMS 

WRITER    AND    EXPERT   ON    CARPENTRY    AND    BUILDING 

PART  II— THE  STEEL  SQUARE 
By  MORRIS  WILLIAMS 


ILLUSTRATED 


CHICAGO 

AMERICAN  TECHNICAL  SOCIETY 
1917 


UOPTRIQHT,  1910,  1916,    BY 

AMERICAN  TECHNICAL  SOCIETY 


COPYRIGHTED  IN   GREAT  BRITAIN 
ALL  RIGHTS  RESERVED 


INTRODUCTION 


/^VN  ENTERING  a  building,  almost  the  first  thing  that  meets 
the  eye  is  the  staircase  and  unconsciously  it  is  made  to  serve 
as  an  indicator  of  the  quality  of  the  architecture.  If  the  design 
is  poor  or  the  construction  faulty,  this  flaw  immediately  gives 
the  visitor  a  bad  impression  of  the  whole  building.  Further- 
more, stairbuilding  is  a  rather  difficult  subject  and  the  princi- 
ples involved  are  very  little  understood,  which  is  evidenced  by 
the  fact  that  the  layouts  as  furnished  by  architects  in  their 
plans  are  often  improperly  done. 

Probably  more  mistakes  occur  in  connection  with  the  stair- 
way of  a  building  than  with  any  other  construction  feature.  It 
is  with  the  idea,  therefore,  of  giving  a  complete  though  simple 
presentation  of  the  construction  methods  as  'applied  to  stand- 
ard design  of  staircases,  that  this  book  has  been  prepared. 

The  article  discusses  straight  and  winding  stairs,  stairs 
with  well  hole,  layouts  for  curved  turns,  the  proper  proportions 
of  rise  and  width  of  tread,  the  design  of  hand  railings  and  many 
other  problems,  the  solution  of  which  will  be  found  very  useful. 

Coupled  with  this  article  is  a  most  instructive  section  on 
the  Steel  Square,  containing  many  applications  of  this  useful 
instrument  to  roof  and  other  types  of  construction. 


CONTENTS 


PART  I 
STAIR-BUILDING 

PAGE 

Stair  construction 1 

Definitions 2 

Setting  out  stairs 8 

Pitch-board 10 

Well-hole 18 

Laying  out  close-string  stair 22 

Open-newel  stairs 32 

Stairs  with  curved  turns 34 

Geometrical  stairways  and  handrailings 43 

Wreaths 43 

Tangent  system 44 

Bevels  to  square  wreaths 60 

How  to  put  curves  on  face-mold 08 

Arrangement  of  risers 74 

PART  II 

STEEL  SQUARE 

Introductory 1 

Specifications  for  steel  square 1 

Miter  and  length  of  side  of  polygon 4 

Steel  square  in  roof  framing 7 

General  problems 8 

Heel  cut  of  common  rafter 13 

Hips 13 

Heel  cut  of  hips  and  valleys 16 


HALL  AND  PARTIALLY  ENCLOSED  STAIRCASE  IN  LONG  HALL,  GREYROCKS, 

ROCKPORT,  MASS. 
Frank  Chouteau  Brown,  Architect,  Boston,  Mass. 


PART   I 

STAIR-BUILDING 


Introductory.  In  the  following  instructions  in  the  art  of  Stair- 
building,  it  is  the  intention  to  adhere  closely  to  the  practical  phases 
of  the  subject,  and  to  present  only  such  matter  as  will  directly  aid 
the  student  in  acquiring  a  practical  mastery  of  the  art. 

Stair-building,  though  one  of  the  most  important  subjects  con- 
nected with  the  art  of  building,  is  probably  the  subject  least  under- 
stood by  designers  and  by  workmen  generally.  In  but  few  of  the 
plans  that  leave  the  offices  of  Architects,  are  the  stairs  properly  laid 
down;  and  many  of  the  books  that  have  been  sent  out  for  the  purpose 
of  giving  instruction  in  the  art  of  building,  have  this  common  defect 
— that  the  body  of  the  stairs  is  laid  down  imperfectly,  and  therefore 
presents  great  difficulties  in  the  construction  of  the  rail. 

The  stairs  are  an  important  feature  of  a  building.  On  entering 
a  house  they  are  usually  the  first  object  to  meet  the  eye  and  claim 
the  attention.  If  one  sees  an  ugly  staircase,  it  will,  in  a  measure, 
condemn  the  whole  house,  for  the  first  impression  produced  will 
seldom  be  totally  eradicated  by  commendable  features  that  may  be 
noted  elsewhere.  It  is  extremely  important,  therefore,  that  both 
designer  and  workman  shall  see  that  staircases  are  properly  laid  out. 

Stairways  should  be  commodious  to  ascend — inviting  people, 
as  it  were,  to  go  up.  When  winders  are  used,  they  should  extend 
past  the  spring  line  of  the  cylinder,  so  as  to  give  proper  width  at 
the  narrow  end  (see -Fig.  72)  and  bring  the  rail  there  as  nearly  as 
possible  to  the  same  pitch  or  slant  as  the  rail  over  the  square  steps. 
When  the  hall  is  of  sufficient  width,  the  stairway  should  not  be  less 
than  four  feet  wide,  so  that  two  people  can  conveniently  pass  each 
other  thereon.  The  height  of  riser  and  width  of  tread  are  governed 
by  the  staircase,  which  is  the  space  allowed  for  the  stairway;  but, 
as  a  general  rule,  the  tread  should  not  be  less  than  nine  inches  wide, 
and  the  riser  should  not  be  over  eight  inches  high.  Seven-inch  riser 


2  STAIR-BUILDING 

and  eleven-inch  tread  will  make  an  easy  stepping  stairway.  If  you 
increase  the  width  of  the  tread,  you  must  reduce  the  height  of  the  riser. 
The  tread  and  riser  together  should  not  be  over  eighteen  inches, 
and  not  less  than  seventeen  inches.  These  dimensions,  however, 
cannot  always  be  adhered  to,  as  conditions  will  often  compel  a  devia- 
tion from  the  rule;  for  instance,  in  large  buildings,  such  as  hotels, 
railway  depots,  or  other  public  buildings,  treads  are  often  made  18 

inches  wide,  having  risers  of  from 
1\  inches  to  5  inches  depth. 

Definitions.  Before  pro- 
ceeding further  with  the  subject, 
it  is  essential  that  the  student 
make  himself  familiar  with  a  few 
of  the  terms  used  in  stair-building. 
The  term  rise  and  run  is 
often  used,  and  indicates  certain 


Pig.  i.  illustrating  Rise,  Run,  and          dimensions  of  the  stairway.    Fig. 

1  will  illustrate   exactly  what  is 

meant;  the  line  A  B  shows  the  run,  or  the  length  over  the  floor  the 
stairs  will  occupy.  From  B  to  C  is  the  rise,  or  the  total  height  from 
top  of  lower  floor  to  top  of  upper  floor.*  The  line  D  is  the  pitch  or 
line  of  nosings,  showing  the  angle  of  inclination  of  the  stairs.  On 
the  three  lines  shown — the  run,  the  rise,  and  the  pitch — depends 
the  whole  system  of  stair-building. 

The  body  or  staircase  is  the  room  or  space  in  which  the  stairway 
is  contained.  This  may  be  a  space  including  the  width  and  length 
of  the  stairway  only,  in  which  case  it  is  called  a  close  stairway,  no  rail 
or  baluster  being  necessary.  Or  the  stairway  may  be  in  a  large 
apartment,  such  as  a  passage  or  hall,  or  even  in  a  large  room,  openings 
being  left  in  the  upper  floors  so  as  to  allow  road  room  for  persons  on 
the  stairway,  and  to  furnish  communication  between  the  stairways 
and  the  different  stories  of  the  building.  In  such  cases  we  have  what 
are  known  as  open  stairways,  from  the  fact  that  they  are  not  closed 
on  both  sides,  the  steps  showing  their  ends  at  one  side,  while  on  the 
other  side  they  are  generally  placed  against  the  wall. 

Sometimes  stairways  are  left  open  on  both  sides,  a  practice  not 

*NOTE.— The  measure  for  the  rise  of  a  stairway  must  always  be  taken  from  the  top 
of  one  floor  to  the  top  of  the  next. 


STAIR-BUILDING  3 

uncommon  in  hotels,  public  halls,  and  steamships.  When  such  stairs 
are  employed,  the  openings  in  the  upper  floor  should  be  well  trimmed 
with  joists  or  beams  somewhat  stronger  than  the  ordinary  joists  used 
in  the  same  floor,  as  will  be  explained  further  on. 

Tread.  This  is  the  horizontal,  upper  surface  of  the  step,  upon 
which  the  foot  is  placed.  In  other  words,  it  is  the  piece  of  material 
that  forms  the  step,  and  is  generally  from  l\  to  3  inches  thick,  and 
made  of  a  width  and  length  to  suit  the  position  for  which  it  is  intended. 
In  small  houses,  the  treads  are  usually  made  of  f -inch  stuff. 

Riser.  This  is  the  vertical  height  of  the  step.  The  riser  is  gen- 
erally made  of  thinner  stuff  than  the  tread,  and,  as  a  rule,  is  not  so 
heavy.  Its  duty  is  to  connect  the  treads  together,  and  to  give  the 
stairs  strength  and  solidity. 

Rise  and  Run.  This  term,  as  already  explained,  is  used  to  indi- 
cate the  horizontal  and  vertical  dimensions  of  the  stairway,  the  rise 
meaning  the  height  from  the  top  of  the  lower  floor  to  the  top  of  the 
second  floor;  and  the  run  meaning  the  horizontal  distance  from  the 
face  of  the  first  riser  to  the  face  of  the  last  or  top  riser,  or,  in  other 
words,  the  distance  between  the  face  of  the  first  riser  and  the  point 
where  a  plumb  line  from  the  face  of  the  top  riser  would  strike  the  floor. 
It  is,  in  fact,  simply  the  distance  that  the  treads  would  make  if  put 
side  by  side  and  measured  together — without,  of  course,  taking  in 
the  nosings. 

Suppose  there  are  fifteen  treads,  each  being  11  inches  wide; 
this  would  make  a  run  of  15  X  11  =  165  inches  =  13  feet  9  inches. 
Sometimes  this  distance  is  called  the  going  of  the  stair ;  this,  however, 
is  an  English  term,  seldom  used  in  America,  and  when  used,  refers 
as  frequently  to  the  length  of  the  single  tread  as  it  does  to  the  run  of 
the  stairway. 

String-Board.  This  is  the  board  forming  the  side  of  the  stairway, 
connecting  with,  and  supporting  the  ends  of  the  steps.  Where  the 
steps  are  housed,  or  grooved  into  the  board,  it  is  known  by  the  term 
housed  string;  and  when  it  is  cut  through  for  the  tread  to  rest  upon, 
and  is  mitered  to  the  riser,  it  is  known  by  the  term  cut  and  mitcrcd 
string.  The  dimensions  of  the  lumber  generally  used  for  the  purpose 
in  practical  work,  are  9\  inches  width  and  |  inch  thickness.  In  the 
first-class  stairways  the  thickness  is  usually  1£  inches,  for  both  front 
and  wall  strings. 


STAIR-BUILDING 


Fig.  2  shows  the  manner  in  which  most  stair-builders  put  their 
risers  and  treads  together.  T  and  T  show  the  treads;  R  and  R,  the 
risers;  S  and  S,  the  string;  0  and  O,  the 
cove  mouldings  under  the  nosings  X  and 
X.  B  and  B  show  the  blocks  that  hold 
the  treads  and  risers  together;  these 
blocks  should  be  from  4  to  6  inches 
long,  and  made  of  very  dry  wood ;  their 
section  may  be  from  1  to  2  inches  square. 
On  a  tread  3  feet  long,  three  of  these 
blocks  should  be  used  at  about  equal 
distances  apart,  putting  the  two  outside 
ones  about  6  inches  from  the  strings. 
They  are  glued  up  tight  into  the  angle. 
First  warm  the  blocks;  next  coat  two  adjoining  sides  with  good,  strong 
glue;  then  put  them  in  position,  and  nail  them  firmly  to  both  tread 
and  riser.  It  will  be  noticed  that  the  riser  has  a  lip  on  the  upper 
edge,  which  enters  into  a  groove  in  the  tread.  This  lip  is  generally 


Fig.  2.    Common  Method  of  Join- 
ing Risers  and  Treads. 


Fig.  3.  Vertical  Section      Fig.  4.  End  Section       Fig.  5.  End  Section 
of  Stair  Steps.  of  Riser.  of  Tread. 

about  f  inch  long,  and  may  be  f  inch  or  £  inch  in  thickness.  Care 
must  be  taken  in  getting  out  the  risers,  that  they  shall  not  be  made 
too  narrow,  as  allowance  must  be  made  for  the  lip. 

If  the  riser  is  a  little  too  wide,  this  will  do  no  harm,  as  the  over- 
width  may  hang  down  below  the  tread ;  but  it  must  be  cut  the  exact 
width  where  it  rests  on  the  string.  The  treads  must  be  made  the 
exact  width  required,  before  they  are  grooved  or  have  the  nosing 


STAIR-BUILDING 


Fig.  6.   Side  Elevation  of  Finish 

ed  Steps  with  Return 

Nosings   and   Cove 

Moulding. 


worked  on  the  outer  edge.    The  lip  or  tongue  on  the  riser  should  fit 
snugly  in  the  groove,  and  should  bottom.     By  following  these  last 
instructions  and  seeing  that  the  blocks  are 
well  glued  in,  a  good  solid  job  will  be  the 
result. 

Fig.  3  is  a  vertical  section  of  stair 
steps  in  which  the  risers  are  shown 
tongued  into  the  under  side  of  the  tread, 
as  in  Fig.  2,  and  also  the  tread  tongued 
into  the  face  of  the  riser.  This  last 
method  is  in  general  use  throughout  the 
country.  The  stair-builder,  when  he  has 
steps  of  this  kind  to  construct,  needs  to 
be  very  careful  to  secure  the  exact  width 

for  tread  and  riser,  including  the  tongue  on  each.  The  usual 
method,  in  getting  the  parts  prepared,  is  to  make  a  pattern  show- 
ing the  end  section  of  each.  The  millman,  with  these  patterns 
to  guide  him,  will  be  able  to  run  the  material  through  the  machine 
without  any  danger  of  leaving  it  either  too  wide  or  too  narrow;  while, 
if  he  is  left  to  himself  without  patterns,  he  is  liable  to  make  mistakes. 
These  patterns  are  illustrated  in  Figs.  4  and  5  respectively,  and,  as 
shown,  are  merely  end  sections  of  riser  and  tread. 

Fig.  6  is  a  side  elevation  of  the  steps  as  finished,  with  return 
nosings  and  cove  moulding  complete. 

A  front  elevation  of  the  finished  step 
is  shown  in  Fig.  7,  the  nosing  and  riser 
returning  against  the  base  of  the  newel  post. 
Often  the  newel  post  projects  past  the 
riser,  in  front;  and  when  such  is  the  case, 
the  riser  and  nosing  are  cut  square  against 
the  base  of  the  newel. 

Fig.  8  shows  a  portion  of  a  cut  and 
mitered  string,  which  will  give  an  excellent 
idea  of  the  method  of  construction.  The 

letter  O  shows  the  nosing,  F  the  return  nosing  with  a  bracket  termi- 
nating against  it.  These  brackets  are  about  j5ff  inch  thick,  and  are 
planted  (nailed)  on  the  string;  the  brackets  miter  with  the  ends  of 
the  risers;  the  ends  of  the/  brackets  which  miter  with  the  risers,  are 


Fig.  7.  Front  Elevation  of 
Finished  Steps. 


6 


STAIR-BUILDING 


Fig.  8.    Portion  of  a  Cut  and  Mitered 

String,  Showing  Method  of 

Constructing  Stairs. 


to  be  the  same  height  as  the  riser.     The   lower  ends  of  two  balus- 
ters are  shown  at  G  G;  and  the  dovetails  or  mortises  to  receive  these 
are  shown  at  E  E.     Generally  two  balusters  are  placed  on  each 
tread,  as  shown;  but  there  are  some- 
times instances  in  which  three  are  used, 
while  in  others  only  one  baluster  is 
made  use  of. 

An  end  portion  of  a  cut  and 
mitered  string  is  shown  in  Fig.  9,  with 
part  of  the  string  taken  away,  show- 
ing the  carriage  —  a  rough  piece  of 
lumber  to  which  the  finished  string  is 
nailed  or  otherwise  fastened.  At  C  is 
shown  the  return  nosing,  and  the  man- 
ner in  which  the  work  is  finished.  A 
rough  bracket  is  sometimes  nailed  on 
the  carriage,  as  shown  at  D,  to  support  the  tread.  The  balusters  are 
shown  dovetailed  into  the  ends  of  the  treads,  and  are  either  glued  or 
nailed  in  place,  or  both.  On  the  lower  edge  of  string,  at  B,  is  a  return 
bead  or  moulding.  It  will  be  noticed  that  the  rough  carriage  is  cut  in 
snugly  against  the  floor  joist. 
Fig.  10  is  a  plan  of  the  portion 
of  a  stairway  shown  in  Fig.  9. 
Here  the  position  of  the  string, 
bracket,  rise'r,  and  tread  can  be 
seen.  At  the  lower  step  is  shown 
how  to  miter  the  riser  to  the 
string;  and  at  the  second  step  is 
shown  how  to  miter  it  to  the 
bracket. 

Fig.  11  shows  a  quick  method 
of  marking  the  ends  of  the  treads 
for  the  dovetails  for  balusters. 
The  templet  A  is  made  of  some 
thin  material,  preferably  zinc  or 

hardwood.  The  dovetails  are  outlined  as  shown,  and  the  intervening 
portions  of  the  material  are  cut  away,  leaving  the  dovetail  portions 
solid.  The  templet  is  then  nailed  or  screwed  to  a  gauge-block  E, 


Fig.  9.    End  Portion  of  Cut  and  Mitered 

String,  with  Part  Removed  to 

Show  Carriage. 


STAIR-BUILDING 


o 

Fig.  10.    Plan  of  Portion  of  Stair. 


when  the  whole  is  ready  for  use.    The  method  of  using  is  clearly 
indicated  in  the  illustration. 

Strings.  There  are  two  main  kinds  of  stair  strings — wall  strings 
and  cut  strings.  These  are  divid- 
ed, again,  under  other  names,  as 
housed  strings,  notched  strings, 
staved  strings,  and  rough  strings. 
Wall  strings  are  the  supporters 
of  the  ends  of  the  treads  and 
risers  that  are  against  the  wall; 
these  strings  may  be  at  both  ends  of 
the  treads  and  risers,  or  they  may  be  at  one  end  only.  They  may  be 
housed  (grooved)  or  left  solid.  When  housed,  the  treads  and  risers 
are  keyed  into  them,  and  glued  and  blocked.  When  left  solid,  they 
have  a  rough  string  or  carriage  spiked  or  screwed  to  them,  to  lend 
additional  support  to  the  ends  of  risers  and  treads.  Stairs  made  after 
this  fashion  are  generally  of  a  rough,  strong  kind,  and  are  especially 
adapted  for  use  in  factories,  shops,  and  warehouses,  where  strength 
and  rigidity  are  of  more  importance  than  mere  external  appearance. 
Open  strings  are  outside  strings  or  supports,  and  are  cut  to  the 
proper  angles  for  receiving  the  ends  of 
the  treads  and  risers.  It  is  over  a  string 
of  this  sort  that  the  rail  and  balusters 
range;  it  is  also  on  such  a  string  that  al 
nosings  return ;  hence,  in  some  localities, 
an  open  string  is  known  as  a  return  string. 
Housed  strings  are  those  that  have 
grooves  cut  in  them  to  receive  the  ends  of 
treads  and  risers.  As  a  general  thing,  wall  strings  are  housed.  The 
housings  are  made  from  f  to  f  inch  deep,  and  the  lines  at  top  of  tread 
and  face  of  riser  are  made  to  correspond  with  the  lines  of  riser  and 
tread  when  in  position.  The  back  lines  of  the  housings  are  so 
located  that  a  taper  wedge  may  be  driven  in  so  as  to  force  the  tread 
and  riser  close  to  the  face  shoulders,  thus  making  a  tight  joint. 

Rough  siring*  are  cut  from  undressed  plank,  and  are  used  for 
strengthening  the  stairs.  Sometimes  a  combination  of  rough-cut 
strings  is  used  for  circular  or  geometrical  stairs,  and,  when  framed 
together,  forms  the  support  or  carriage  of  the  stairs. 


Fig.  11.    Templet  Used  to  Mark 

Dovetail  Cuts   for 

Balusters. 


8  STAIR-BUILDING 

Staved  strings  are  built-up  strings,  and  are  composed  of  narrow 
pieces  glued,  nailed,  or  bolted  together  so  as  to  form  a  portion  of  a 
cylinder.  These  are  sometimes  used  for  circular  stairs,  though  in 
ordinary  practice  the  circular  part  of  a  string  is  a  part  of  the  main 
string  bent  around  a  cylinder  to  give  it  the  right  curve. 

Notched  strings  are  strings  that  carry  only  treads.  They  are 
generally  somewhat  narrower  than  the  treads,  and  are  housed  across 
their  entire  width.  A  sample  of  this  kind  of  string  is  the  side  of  a 
common  step-ladder.  Strings  of  this  sort  are  used  chiefly  in  cellars, 
or  for  steps  intended  for  similar  purposes. 

Setting  Out  Stairs.  In  setting  out  stairs,  the  first  thing  to  do  is 
to  ascertain  the  locations  of  the  first  and  last  risers,  with  the  height 
of  the  story  wherein  the  stair  is  to  be  placed.  These  points  should  be 
marked  out,  and  the  distance  between  them  divided  off  equally, 
giving  the  number  of  steps  or  treads  required.  Suppose  we  have 
between  these  two  points  15  feet,  or  180  inches.  If  we  make  our 
treads  10  inches  wide,  we  shall  have  18  treads.  It  must  be  remembered 
that  the  number  of  risers  is  always  one  more  than  the  number  of  treads, 
so  that  in  the  case  before  us  there  will  be  19  risers. 

The  height  of  the  story  is  next  to  be  exactly  determined,  being 
taken  on  a  rod.  Then,  assuming  a  height  of  riser  suitable  to  the  place, 
we  ascertain,  by  division,  how  often  this  height  of  riser  is  contained 
in  the  height  of  the  story;  the  quotient,  if  there  is  no  remainder, 
will  be  the  number  of  risers  in  the  story.  Should  there  be  a  remainder 
on  the  first  division,  the  operation  is  reversed,  the  number  of  inches 
in  the  height  being  made  the  dividend,  and  the  before-found  quotient, 
the  divisor.  The  resulting  quotient  will  indicate  an  amount  to  be 
added  to  the  former  assumed  height  of  riser  for  a  new  trial  height. 
The  remainder  will  now  be  less  than  in  the  former  division;  and  if 
necessary,  the  operation  of  reduction  by  division  is  repeated,  until 
the  height  of  the  riser  is  obtained  to  the  thirty-second  part  of  an  inch. 
These  heights  are  then  set  off  on  the  story  rod  as  exactly  as  possible. 

The  story  rod  is  simply  a  dressed  or  planed  pole,  cut  to  a  length 
exactly  corresponding  to  the  height  from  the  top  of  the  lower  floor 
to  the  top  of  the  next  floor.  Let  us  suppose  this  height  to  be  11  feet 
1  inch,  or  133  inches.  Now,  we  have  19  risers  to  place  in  this  space, 
to  enable  us  to  get  upstairs;  therefor,  if  we  divide  133  by  19,  we 
get  7  without  any  remainder.  Seven  inches  will  therefore  be  the 


STAIR-BUILDING  9 

width  or  height  of  the  riser.  Without  figuring  this  out,  the  workman 
may  find  the  exact  width  of  the  riser  by  dividing  his  story  rod,  by 
means  of  pointers,  into  19  equal  parts,  any  one  part  being  the  proper 
width.  It  may  be  well,  at  this  point,  to  remember  that  the  first  riser 
must  always  be  narrower  than  the  others,  because  the  thickness  of  the 
first  tread  must  be  taken  off. 

The  width  of  treads  may  also  be  found  without  figuring,  by 
pointing  off  the  run  of  the  stairs  into  the  required  number  of  parts; 
though,  where  the  student  is  qualified,  it  is  always  better  to  obtain 
the  width,  both  of  treads  and  of  risers,  by  the  simple  arithmetical 
rules. 

Having  determined  the  width  of  treads  and  risers,  a  pitch-board 
should  be  formed,  showing  the  angle  of  inclination.  This  is  done  by 
cutting  a  piece  of  thin  board  or  metal  in  the  shape  of  a  right-angled 
triangle,  with  its  base  exactly  equal  to  the  run  of  the  step,  and  its 
perpendicular  equal  to 
the  height  of  the  riser. 
It  is  a  general  maxim, 
that  the  greater  the 
breadth  of  a  step  or  tread, 
the  less  should  be  the 
height  of  the  riser;  and, 
conversely,  the  less  the 
breadth  of  a  step,  the 

Fig.  12.    Graphic  Illustration  of  Proportional  Dimen- 
greater    should      be      the  sions  of  Treads  and  Risers. 

height  of  the  riser.    The 

proper  relative  dimensions  of  treads  and   risers  may  be  illustrated 

graphically,  as  in  Fig.  12. 

In  the  right-angle  triangle  ABC,  make  A  B  equal  to  24  inches, 
and  B  C  equal  to  1 1  inches — the  standard  proportion.  Now,  to  find 
the  riser  corresponding  to  a  given  width  of  tread,  from  B,  set  off  on 
A  B  the  width  of  the  tread,  as  B  D;  and  from  D,  erect  a  perpendicular 
D  E,  meeting  the  hypotenuse  in  E;  then  D  E  is  the  height  of  the  riser; 
and  if  we  join  B  and  E,  the  angle  D  B  E  is  the  angle  of  inclination, 
showing  the  slope  of  the  ascent.  In  like  manner,  where  B  F  is  the 
width  of  the  tread,  F  G  is  the  riser,  and  B  G  the  slope  of  the  stair. 
A  width  of  tread  B  II  gives  a  riser  of  the  height  of  H  K;  and  a  width 
of  tread  equal  to  B  L  gives  a  riser  equal  to  L  M, 


10  STAIR-BUILDING 

In  the  opinion  of  many  builders,  however,  a  better  scheme  of 
proportions  for  treads  and  risers  is  obtained  by  the  following  method : 

Set  down  two  sets  of  numbers,  each  in  arithmetical  progression — 
the  first  set  showing  widths  of  tread,  increasing  by  inches;  the  other 
showing  heights  of  riser,  decreasing  by  half-inches. 

TREADS,  INCHES  RISERS,  INCHES 

5  9 

6  8} 

7  8 

8  .  7J 

9  7 

10  61 

11  6 

12  51 

13  5 

14  41 

15  4 

16  31 

17  3 

18  21       N 

It  will  readily  be  seen  that  each  pair  of  treads  and  risers  thus  obtained 
is  suitably  proportioned  as  to  dimensions. 

It  is  seldom,  however,  that  the  proportions  of  treads  and  risers 
are  entirely  a  matter  of  choice.  The  space  allotted  to  the  stairs  usually 
determines  this  proportion ;  but  the  above  will  be  found  a  useful  stand- 
ard, to  which  it  is  desirable  to  approximate. 

In  the  better  class  of  buildings,  the  number  of  steps  is  considered 
in  the  plan,  which  it  is  the  business  of  the  Architect  to  arrange;  and 
in  such  cases,  the  height  of  the  story  rod  is  simply  divided  into  the 
number  required. 

Pitch-Board.  It  will  now  be  in  order  to  describe  a  pitch-board 
and  the  manner  of  using  it;  no  stairs  can  be  properly  built  without 
the  use  of  a  pitch-board  in  some  form  or  other.  Properly  speaking, 
a  pitch-board,  as  already  explained,  is  a  thin  piece  of  material, 
generally  pine  or  sheet  metal,  and  is  a  light-angled  triangle  in  outline. 
One  of  its  sides  is  made  the  exact  height  of  the  rise;  at  right  angles 
with  this  line  of  rise,  the  exact  width  of  the  tread  is  measured  off; 
and  the  material  is  cut  along  the  hypotenuse  of  the  right-angled 
triangle  thus  formed. 

The  simplest  method  of  making  a  pitch-board  is  by  using  a  steel 


STAIR-BUILDING 


11 


Fig.  13.    Steel  Square  Used  as  a  Pitch 

Board  in  Laying  Out  Stair 

String. 


square,  which,  of  course,  every  carpenter  in  this  country  is  supposed 

to  possess.    By  means  of  this  invaluable  tool,  also,  a  stair  string  can 

be  laid  out,  the  square  being  applied  to  the  string  as  shown  in  Fig.  13. 

In  the  instance  here  illustrated,  the 
square  shows  10  inches  for  the 
tread  and  7  inches  for  the  rise. 

To  cut  a  pitch-board,  after  the 
tread  and  rise  have  been  deter- 
mined, proceed  as  follows:  Take 
a  piece  of-  thin,  clear  material,  and 
lay  the  square  on  the  face  edge,  as 
shown  in  Fig.  13.  Mark  out  the 

pitch-board  with  a  sharp  knife;  then  cut  out  with  a  fine  saw,  and 

dress  to  the  knife  marks;  nail  a  piece  on  the  largest  edge  of  the  pitch- 
board  for  a  gauge  or  fence,  and  it  is  ready  for  use. 

Fig.  14  shows  the  pitch-board  pure  and  simple;  it  may  be  half 

an  inch  thick,  or,  if  of  hardwood,  may  be  from  a  quarter-inch  to  a 

half-inch  thick. 

Fig.  15  shows  the  pitch-board  after  the  gauge  or  fence  is  nailed  on. 

This  fence  or  gauge  may  be  about  1  £  inches,  wide  and  from  f  to  f 

inch  thick ." 

Fig.  16  shows  a  sectional  view  of  the  pitch-board  with  a  fence 

nailed  on. 

In  Fig.  17  the  manner  of  applying  the  pitch-board  is  shown. 

R  R  R  is  the  string,  and  the  line  A  shows  the  jointed  or  straight  edge 

of    the    string.      The 

pitch-board    P     is 

shown  in  position,  the 

line  8J  represents  the 

step  or  tread,  and  the 

line  7f  shows  the  line 

of   the    riser.     These 

two  lines  are  of  course 

at  right  angles,  or,  as  the  carpenter   would   say;  they  are  square. 

This  string  shows  four   complete  cuts,  and  part  of  a  fifth  cut  for 

treads,  and  five  complete  cuts  for  risers.     The  bottom  of  the  string 

at  W  is  cut  off  at  the  line  of  the  floor  on  which  it  is  supposed  to 
rest.    The  line  C  is  the  line  of  the  first  riser.     This  riser  is  cut  lower 


Fig.  14. 


Fig.  15. 


Fig.  1& 


Showing  How  a  Pitch-Board  is  Made. 

Fig.  15  shows  Kange  fastened  to  long  edge;  Fig.  16  is  a 

sectional  elevation  of  completed  board 


12  STAIR-BUILDING 

than  any  of  the  other  risers,  because,  as  above  explained,  the  thick- 
ness of  the  first  tread  is  always  taken  off  it;  thus,  if  the  tread  is  1| 
inches  thick,  the  riser  in  this  .case  would  only  require  to  be  6£  inches 
wide,  as  7f  -  U  =  6£. 

The  string  must  be  cut  so  that  the  line  at  W  will  be  only  6J 
inches  from  the  line  at  8^,  and  these  two  lines  must  be  parallel. 
The  first  riser  and  tread  having  been  satisfactorily  dealt  with,  the 
rest  can  easily  be  marked  off  by  simply  sliding  the  pitch-board  along 
the  line  A  until  the  outer  end  of  the  line  8^  on  the  pitch-board 
strikes  the  outer  end  of  the  line  7f  on  the  string,  when  another  tread 
and  another  riser  are  to  be  marked  off.  The  remaining  risers  and 
treads  are  marked  off  in  the  same  manner. 

Sometimes  there  may  be  a  little  difficulty  at  the  top  of  the  stairs, 

in  fitting  the  string  to  the 
trimmer  or  joists;  but,  as  it 

*s  necessarv  first  t°  become 
expert  with  the  pitch-board, 

Fig.  1       Showing  Method  of  Using  Pitch-Boar         the  ^^    °f   trimming    ** 

well  or  attaching  the  cylinder 
to  the  string  will  be  left  until  other  matters  have  been  discussed. 

Fig.  18  shows  a  portion  of  the  stairs  in  position.  *S  and  *S  show 
the  strings,  which  in  this  case  are  cut  square;  that  is,  the  part  of  the 
string  to  which  the  riser  is  joined  is  cut  square  across,  and  the  butt  or 
end  wood  of  the  riser  is  seen.  In  this  case,  also,  the  end  of  the  tread 
is  cut  square  off,  and  flush  with  the  string  and  riser.  Both  strings 
in  this  instance  are  open  strings.  Usually,  in  stairs  of  this  kind,  the 
ends  of  the  treads  are  rounded  off  similarly  to  the  front  of  the  tread, 
and  the  ends  project  over  the  strings  the  same  distance  that  the  front 
edge  projects  over  the  riser.  If  a  moulding  or  cove  is  used  under  the 
nosing  in  front,  it  should  be  carried  round  on  the  string  to  the  back 
edge  of  the  tread  and  cut  off  square,  for  in  this  case  the  back  edge  of 
the  tread  will  be  square.  A  riser  is  shown  at  R,  and  it  will  be  noticed 
that  it  runs  down  behind  the  tread  on  the  back  edge,  and  is  either 
nailed  or  screwed  to  the  tread.  This  is  the  American  practice,  though 
in  England  the  riser  usually  rests  on  the  tread,  which  extends  clear 
back  to  string  as  shown  at  the  top  tread  in  the  diagram.  It  is  much 
better,  however,  for  general  purposes,  that  the  riser  go  behind  the 
tread,  as  this  tends  to  make  the  whole  stairway  much  stronger. 


STAIR-BUILDING 


13 


Fig.  18.    Portion  of  Stair  in  Position. 


Housed  strings  are  those  which  carry  the  treads  and  risers  without 
their  ends  being  seen.  In  an  open  stair,  the  wall  string  only  is  housed, 
the  other  ends  of  the  treads  and  risers  resting  on  a  cut  string,  and  the 

nosings  and  mouldings 
being  returned  as  be- 
fore described. 

The  manner  of 
housing  is  shown  in 
Fig.  19,  in  which  the 
treads  T  T  and  the 
risers  R  R  are  shown 
in  position,  secured  in 
place  respectively  by 
nleans  of  wedges  X  X 
and  F  F,  which  should 
be  well  covered  with 
good  glue  before  insertion  in  the  groove.  The  housings  are 
generally  made  from  \  to  f  inch  deep,  space  for  the  wedge  being  cut 
to  suit. 

In  some  closed  stairs  in  which  there  is  a  housed  string  between  the 
newels,  the  string  is  double-tenoned  into  the  shanks  of  both  newels, 
as  shown  in  Fig.  20.  The  string  in  this  example  is  made  12|  inches 
wide,  which  is  a  very  good  width 
for  a  string  of  this  kind;  but  the 
thickness  should  never  be  less  than 
1  \  inches.  The  upper  newel  is  made 
about  5  feet  4  inches  long  from  drop 
to  top  of  cap.  These  strings  are 
generally  capped  with  a  subrail  of 
some  kind,  on  which  the  baluster, 
if  any,  is  cut-mitered  in.  Generally 
a  groove,  the  width  of  the  square 
of  the  balusters,  is  worked  on  the 
top  of  the  subrail,  and  the  balusters  are  worked  out  to  fit  into  this 
groove;  then  pieces  of  this  material,  made  the  width  of  the  groove 
and  a  little  thicker  than  the  groove  is  deep,  are  cut  so  as  to  fit  in 
snugly  between  the  ends  of  the  balusters  resting  in  the  groove.  This 
makes  a  solid  job;  and  the  pieces  between  the  balusters  may  be  inside 


Showing  Method  of  Housing 
Treads  and  Risers. 


14 


STAIR-BUILDING 


of  any  shape  on  top,  either  beveled,  rounded,  or  moulded,  in  which 
case  much  is  added  to  the  appearance  of  the  stairs. 

Fig.  21  exhibits  the  method  of  attaching  the  rail  and  string  to 
the  bottom  newel.  The  dotted  lines 
indicate  the  form  of  the  tenons  cut  to 
fit  the  mortises  made  in  the  newel  to 
receive  them. 

Fig.   22  shows  how  the  string  fits 


against  the  newel  at  the  top; 
also  the  trimmer  E,  to  which  the 
newel  post  is  fastened.  The 
string  in  this  case  is  tenoned  into 

,  ,     ,,  Fig.  20.    Showing  Method  of  Con- 

the  upper  newel  post  the  same         nectmg  Housed  string  to 

Newels. 

way  as  into  the  lower  one. 

The  open  string  shown  in  Fig.  23  is  a  portion 
of  a  finished  string,  showing  nosings  and  cove 
returned  and  finishing  against  the  face  of  the 
string.  Along  the  lower  edge  of  the  string  is 
shown  a  bead  or  moulding,  where  the  plaster 
is  finished. 

A  portion  of  a  stair  of  the  better  class  is 
shown  in-  Fig.  24.  This  is  an  open,  bracketed 
string,  with  returned  nosings  and  coves  and 
scroll  brackets.  These  brackets  arc  made  about 
-£  inch  thick,  and  may  be  in  any  desirable  pat- 
tern. The  end  next  the  riser  should  be  mite  red 
to  suit  ;  this  will  require  the  riser  to  be  f  inch 
longer  than  the  face  of  the  string.  The  upper 
part  of  the  bracket  should  run  under  the  cove 

Fig.  21.  Method  or  connect-    moulding;  and  the  tread  should  project  over 
we'i'8  to       the  string  the  full  f  inch,  so  as  to  cover  the 


ig. 


STAIR-BUILDING 


15 


bracket  and  make  the  fpce  even  for  the  nosing  and  the  cove  moulding 
to  fit  snugly  against  i'ie  end  of  the  tread  and  the  face  of  the  bracket. 
Great  care  must  be  taken  about  this  point,  or  endless  trouble  will 

follow.  In  a  bracketed 
stair  of  this  kind,  care 
must  be  taken  in  plac- 
ing the  newel  posts, 
and  provision  must  be 
made  for  the  extra  £ 
inch  due  to  the  brack- 
et. The  newel  post 
must  be  set  out  from 
the  string  f  inch,  and 
it  will  then  align  with 
the  baluster. 

We  have  now  de- 
scribed several  methods  of  dealing  with  strings;  but  there  are  still  a 
few  other  points  connected  with  these  members,  both  housed  and 
open,  that  it  will  be  necessary  to  explain,  before  the  young  work- 
man can  proceed  to  build  a  fair  flight  of  stairs.  The  connection  of 
the  wall  string  to  the  lower  and  upper  floors,  and  the  manner  of 
affixing  the  outer  or  cut  string  to  the  upper  joist  and  to  the  newel, 


Fig.  22.    Connections  of  String  and  Trimmer  at  Upper 
Newel  Post. 


Fig.  23.    Portion  of  Finished  String, 

Showing  Returned  Nosings 

and  Coves,  also  Bead 

Moulding. 


Fig.  24.    Portion  of  Open,  Bracketed 
String  Stair,  with  Relumed  Nos- 
ings and  Coves.  Scroll  Brack- 
ets, and  Mead  Moulding. 


are  matters  that  must  not  be  overlooked.  It  is  the  intention  to  show 
how  these  things  are  accomplished,  and  how  the  stairs  are  made 
strong  by  the  addition  of  rough  strings  or  bearing  carriages. 


16 


STAIR-BUILDING 


Side  Elevation  of  Part  of 
Stair  with  Open,  Cut  and 
Mitered    String. 


Fig.  25  gives  a  side  view  of  part  of  a  stair  of  the  better  class,  with 

one  open,  cut  and  mitered  string.    In  Fig.  26,  a  plan  of  this  same  stair- 

way, W  S  shows  the  wall  string;  R  S,  the  rough  string,  placed  there 
to  give  the  structure  strength;  and  0 
S,  the  outer  or  cut  and  mitered  string. 
At  A  A  the  ends  of  the  risers  are  shown, 
and  it  will  be  noticed  that  they  are 
mitered  against  a  vertical  or  riser  line 
of  the  string,  thus  preventing  the  end  of 
the  riser  from  being  seen.  The  other 
end  of  the  riser  is  in  the  housing  in  the 
wall  string.  The  outer  end  of  the  tread 
is  also  mitered  at  the  nosing,  and  a  piece 
of  material  made  or  worked  like  the 

nosing  is   mitered   against   or  returned   at  the  end   of  the   tread. 

The  end  of  this  returned  piece  is  again  returned  on  itself  back  to  the 

string,  as  shown  at  N  in  Fig.  25.    The  moulding,  which  is  f-inch 

cove  in  this  case,  is  also  returned  on  itself  back  to  the  string. 

The  mortises  shown  at  B  B  B  B  (Fig.  26),  are  for  the  balusters. 

It  is  always  the  proper  thing  to  saw  the  ends  of  the  treads  ready  for 

the  balusters  before  the  treads  are  attached  to  the  string;  then,  when 

the  time  arrives  to  put  up  the  rail,  the  back  ends  of  the  mortises  can 

be  cut  out,  when  the  treads  will 

be  ready  to  receive  the  balusters. 

The  mortises  are  dovetailed,  and, 

of  course,  the  tenons  on  the  balus- 

ters must  be  made  to  suit.    The 

treads  are  finished  on  the  bench; 

and  the  return  nosings  are  fitted 

to  them  and  tacked  on,  so  that 

they  may  be  taken  off  to  insert 

the  balusters  when  the  rail  is  being 

put  in  position. 

Fig.  27  shows  the  manner  in 


I 

fWS 

1 

B     B 

I      I 

B     B 
1      • 

A 

A 

>~7los 

]  * 

Fig.  26.    Plan  of  Part  of  Stair  Shown  in 
Fig.  25. 


a  wall  string  is  finished  at  the  foot  of  the  stairs.  S  shows  the 
string,  with  moulding  wrought  on  the  upper  edge.  This  moulding 
may  be  a  simple  ogee,  or  may  consist  of  a  number  of  members; 
or  it  may  be  only  a  bead  ;  or,  again,  the  edge  of  the  string  may  be 


STAIR-BUILDING 


17 


Fig.  27.    Showing  How  Wall  String  is  Fin- 
ished at  Foot  of  Stair. 


left  quite  plain;  this  will  be  regulated  in  great  measure  by  the  style  of 

finish  in  the  hall  or  other  part  of  the  house  in  which  the  stairs  are 

placed.    B  shows  a  portion  of  a  baseboard,  the  top  edge  of  which 

has  the  same  finish  as  the  top  edge  of  the  string.     B  and  A  together 

show  the  junction  of  the  string 
and  base.  F  F  show  blocks 
glued  in  the  angles  of  the  steps 
to  make  them  firm  and  solid. 
Fig.  28  shows  the  manner 
in  which  the  wall  string  S  is 
finished  at  the  top  of  the  stairs. 
It  will  be  noticed  that  the 
moulding  is  worked  round  the 
ease-off  at  A  to  suit  the  width 
of  the  base  at  B.  The  string 
is  cut  to  fit  the  floor  and  to 

butt  against  the  joist.    The  plaster  line  under  the  stairs  and  on  the 

ceiling,  is  also  shown. 

Fig.  29  shows  a  cut  or  open  string  at  the  foot  of  a  stairway,  and 

the  manner  of  dealing  with  it  at  its  junction  with  the  newel  post  K. 

The  point  of  the  string  should 

be  mortised  into  the  newel  2 

inches,  3  inches,  or  4  inches, 

as  shown  by  the  dotted  lines; 

and  the  mortise  in  the  newel 

should  be  cut  near  the  center, 

so  that  the  center  of  the  balus- 
ter will   be  directly  opposite 

the  central  line  of  the  newel 

post.      The    proper     way  to 

manage  this,  is  to  mark  the 

central  line  of  the  baluster  on 

the  tread,  and  then  make  this 

line  correspond  with  the  central  line  of  the  newel  post.     By  careful 

attention  to  this  point,  much  trouble  will  be  avoided  where  a  turned 

cap  is  used  to  receive  the  lower  part  of  the  rail. 

The  lower  riser  in  a  stair  of  this  kind  will  be  somewhat  shorter 

than  the  ones  above  it,  as  it  must  be  cut  to  fit  between  the  newel  aod 


Fig.  28.    Showing  How  Wall  String  is  Fin- 
ished  at  Top  of  Stair. 


18 


STAIR-BUILDING 


Square 


the  wall  string.    A  portion  of  the  tread,  as  well  as  of  the  riser,  will 
also  butt  against  the  newel,  as  shown  at  W. 

If  there  is  no  spandrel  or  wall  under  the  open  string,  it  may 
run  down  to  the  floor  as  shown  by  the  dotted  line  at  0.  The  piece 
0  is  glued  to  the  string,  and  the  moulding  is  worked  on  the  curve. 
If  there  is  a  wall  under  the  string  S,  then  the  base  B,  shown  by  the 
dotted  lines,  will  finish  against  the  string,  and  it  should  have  a  mould- 
ing on  its  upper  edge,  the  same  as  that  on  the  lower  edge  of  the  string, 
if  any,  this  moulding  being  mitered  into  the  one  on  the  string.  When 
there  is  a  base,  the  piece  0  is  of  course  dispensed  with. 

The  square  of  the  newel  should  run  down  by  the  side  of  a  joist 
as  shown,  and  should  be  firmly  secured  to  the  joist  either  by  spiking 

or  by  some  other  suitable  device. 
If  the  joist  runs  the  other  way, 
try  to  get  the  newel  post  against 
it,  if  possible,  either  by  furring 
out  the  joist  or  by  cutting  a  por- 
tion off  the  thickness  of  the  newel. 
The  solidity  of  a  stair  and  the 
firmness  of  the  rail,  depend  very 
much  upon  the  rigidity  of  the 
newel  pest.  The  above  sugges- 
tions are  applicable  where  great 
strength  is  required,  as  in  public 
buildings.  In  ordinary  work,  the  usual  method  is  to  let  the  newel  rest 
on  the  floor. 

Fig.  30  shows  how  the  cut  string  is  finished  at  the  top  of  the  stairs. 
This  illustration  requires  no  explanation  after  the  instructions  already 
given. 

Thus  far,  stairs  having  a  newel  only  at  the  bottom  have  been 
dealt  with.  There  are,  however,  many  modifications  of  straight  and 
return  stairs  which  have  from  two  to  four  or  six  newels.  In  such 
cases,  the  methods  of  treating  strings  at  their  finishing  points  must 
necessarily  be  somewhat  different  from  those  described;  but  the 
general  principles,  as  shown  and  explained,  will  still  hold  goo-J. 

Well-Hole.  Before  proceeding  to  describe  and  illustrate  neweled 
stairs,  it  will  be  proper  to  say  something  about  the  well-Iiole,  or  the 


Fig.  29.  Showing  How  a  Cut  or  Open  String 
is  Finished  at  Foot  of  Stair. 


STAIR-BUILDING 


19 


opening  through  the  floors,  through  which  the  traveler  on  the  stairs 
ascends  or  descends  from  one  floor  to  another. 

Fig.  31  shows  a  well-hole,  and  the  manner  of  trimming  it.  In 
this  instance  the  stairs  are  placed  against  the  wall;  but  this  is  not 
necessary  in  all  cases,  as  the  well-hole  may  be  placed  in  any  part  of 
the  building. 

The  arrangement  of  the  trimming  varies  according  as  the  joists 
are  at  right  angles  to,  or  are  parallel  to,  the  wall  against  which  the 
stairs  are  built.  In  the  former  case  (Fig.  31,  ^4)  the  joists  are  cut  short 
and  tusk-tenoned  into  the  heavy  trimmer  T  T,  as  shown  in  the  cut. 
This  trimmer  is  again  tusk-tenoned  into  two  heavy  joists  T  J  and  T  J, 
which  form  the  ends  of  the  well-hole.  These  heavy  joists  are  called 
trimming  joists;  and,  as  they  have  to  carry  a  much  heavier  load  than 
other  joists  on  the  same  floor, 
they  are  made  much  heavier. 
Sometimes  two  or  three  joists 
are  placed  together,  side  by 
side,  being  bolted  or  spiked 
together  to  give  them  the 
desired  unity  and  strength.  In 
constructions  requiring  great 
strength,  the  tail  and  header 

joists    Of    a    Well-hole    are    SUS-         F.g   ^     Showlng  How  a  Cut  or  Open  String 

pended  on  iron  brackets. 

If  the  opening  runs  paral- 
lel with  the  joists  (Fig.  31,  Z?),  the  timber  forming  the  side  of  the 
well-hole  should  be  left  a  little  heavier  than  the  other  joists,  as  it 
will  have  to  carry  short  trimmers  (T  J  and  T  J}  and  the  joists  run- 
ning into  them.  The  method  here  shown  is  more  particularly 
adapted  to  brick  buildings,  but  there  is  no  reason  why  the  same 
system  may  not  be  applied  to  frame  buildings. 

Usually  in  cheap,  frame  buildings,  the  trimmers  T  T  are  spiked 
against  the  ends  of  the  joists,  and  the  ends  of  the  trimmers  are  sup- 
ported by  being  spiked  to  the  trimming  joists  T  J,  T  J.  This  is  not 
very  workmanlike  or  very  secure,  and  should  not  be  done,  as  it  is  not 
nearly  so  strong  or  durable  as  the  old  method  of  framing  the  joists  and 
trimmers  together. 

Fig.  32  shows  a  stair  with  three  newels  and  a  platform.     In  this 


20 


STAIR-BUILDING 


example,  the  first  tread  (No.  1)  stands  forward  of  the  newel  post 
two-thirds  of  its  width.  This  is  not  necessary  in  every  case,  but  it  is 
sometimes  done  to  suit  conditions  in  the  hallway.  The  second  newel 
is  placed  at  the  twelfth  riser,  and  supports  the  upper  end  of  the  first 


TJ. 


T.J. 


Pig.  31.    Showing  Ways  of  Trimming  Well-Hole  when  Joists  Run  in  Different 
Directions. 

cut  string  and  the  lower  end  of  the  second  cut  string.  The  platform 
(12)  is  supported  by  joists  which  are  framed  into  the  wall  and  are 
fastened  against  a  trimmer  running  from  the  wall  to  the  newel  along 
the  line  12.  This  is  the  case  only  when  the  second  newel  runs  down 
to  the  floor. 

If  the  second  newel  does  not  run  to  the  floor,  the  framework 
supporting  the  platform  will  need  to  be  built  on  studding.  The  third 
newel  stands  at  the  top  of  the  stairs,  and  is  fastened  to  the  joists  of 
the  second  floor,  or  to  the  trimmer,  somewhat  after  the  manner  of 
fastening  shown  in  Fig.  29.  In  this  example,  the  stairs  have  16  risers 


STAIR-BUILDING 


21 


and  15  treads,  the  platform  or  landing  (12)  making  one  tread.  The 
figure  16  shows  the  floor  in  the  second  story. 

This  style  of  stair  will  require  a  well-hole  in  shape  about  as 
shown  in  the  plan;  and  where  strength  is  required,  the  newel  at  the 
top  should  run  from  floor  to  floor,  and  act  as  a  support  to  the  joists 
and  trimmers  on  which  the  second  floor  is  laid.  » 

Perhaps  the  best  way  for  a  beginner  to  go  about  building  a  stair- 
way of  this  type,  will  be  to  lay  out  the  work  on  the  lower  floor  in  the 
exact  place  where  the  stairs  are  to  be  erected,  making  everything 


Fig.  32.    Stair  with  Three  Newels  and  a  Platform. 

full  she.  There  will  be  no  difficulty  in  doing  this;  and  if  the  positions 
of  the  first  riser  and  the  three  newel  posts  are  accuratply  defined, 
the  building  of  the  stairs  will  be  an  easy  matter.  Plumb  lines  can  be 
raised  from  the  lines  on  the  floor,  and  the  positions  of  the  platform 
and  each  riser  thus  easily  determined.  Not  only  is  it  best  to  line  out 
on  the  floor  all  stairs  having  more  than  one  newel;  but  in  constructing 
any  kind  of  stair  it  will  perhaps  be  safest  for  a  beginner  to  lay  out  in 
exact  position  on  the  floor  the  points  over  which  the  treads  and  risers 
will  stand.  By  adopting  this  rule,  and  seeing  that  the  strings,  risers, 
and  treads  correspond  exactly  with  the  lines  on  the  floor,  many  cases 
of  annoyance  will  be  avoided.  Many  expert  stair-builders,  in  fact, 
adopt  this  method  in  their  practice,  laying  out  all  stairs  on  the  floor, 
including  even  the  carriage  strings,  and  they  cut  out  all  the  material 
from  the  lines  obtained  on  the  floor.  By  following  this  method,  one 
can  see  exactly  the  requirements  in  each  particular  case,  and  can 
rectify  any  error  without  destroying  valuable  material. 


22  STAIR-BUILDING 

Laying  Out.  In  order  to  afford  the  student  a  clear  idea  of  what 
is  meant  by  laying  out  on  the  floor,  an  example  of  a  simple  close- 
string  stair  is  given.  In  Fig.  33,  the  letter  F  shows  the  floor  line; 
L  is  the  landing  or  platform;  and  W  is  the  wall  line.  The  stair  is  to 
be  4  feet  wide  over  strings;  the  landing,  4  feet  wide;  the  height  from 
floor  to  landing,  7  feet;  and  the  run  from  start  to  finish  of  the  stair,  8 
feet  8 1  inches. 

The  first  thing  to  determine  is  the  dimensions  of  the  treads  and 
risers.  The  wider  the  tread,  the  lower  must  be  the  riser,  as  stated 
before.  No  definite  dimensions  for  treads  and  risers  can  be  given, 
as  the  steps  have  to  be  arranged  to  meet  the  various  difficulties  that 
may  occur  in  the  working  out  of  the  construction;  but  a  common 
rule  is  this:  Make  the  width  of  the  tread,  plus  twice  the  rise,  equal 
to  24  inches.  This  will  give,  for  an  8-inch  tread,  an  8-inch  rise; 
for  a  9-inch  tread,  a  72-inch  rise;  for  a  10-inch  tread,  a  7-inch  rise, 
and  so  on.  Having  the  height  (7  feet)  and  the  run  of  the  flight  (8  feet 
8£  inches),  take  a  rod  about  one  inch  square,  and  mark  on  it  the  height 
from  floor  to  landing  (7  feet),  and  the  length  of  the  going  or  run  of  the 
flight  (8  feet  8.j  inches).  Consider  now  what  are  the  dimensions 
which  can  be  given  to  the  treads  and  risers,  remembering  that  there 
will  be  one  more  riser  than  the  number  of  treads.  Mark  off  on  the 
rod  the  landing,  forming  the  last  tread.  If  twelve  risers  are  desired, 
divide  the  height  (namely,  7  feet)  by  12,  which  gives  7  inches  as  the 
rise  of  each  step.  Then  divide  the  run  (namely,  8  feet  8^  inches)  by 
11,  and  the  width  of  the  tread  is  found  to  be  9}  inches. 

Great  care  must  be  taken  in  making  the  pitch-board  for  marking 
off  the  treads  and  risers  on  the  string.  The  pitch-board  may  be  made 
from  dry  hardwood  about  f  inch  thick.  One  end  and  one  side  must 
be  perfectly  square  to  each  other;  on  the  one,  the  width  of  the  tread 
is  set  off,  and  on  the  other  the  height  of  the  riser.  Connect  the  two 
points  thus  obtained,  and  saw  the  wood  on  this  line.  The  addition 
of  a  gauge-piece  along  the  longest  side  of  the  triangular  piece,  com- 
pletes the  pitch-board,  as  was  illustrated  in  Fig.  15. 

The  length  of  the  wall  and  outer  string  can  be  ascertained  by 
means  of  the  pitch-board.  One  side  and  one  edge  of  the  wall  string 
must  be  squared;  but  the  outer  string  must  be  trued  all  round.  On 
the  strings,  mark  the  p3sitions  of  the  treads  and  risers  by  using  the 
pitch-board  as  already  explained  (Fig.  17).  Strings  are  usually 


STAIR-BUILDING 


23 


made  11  inches  wide,  but  may  be  made  12£  inches  wide  if  necessary 
for  strength. 

After  the  widths  of  risers  and  treads  have  been  determined,  and 
the  string  is  ready  to  lay  out,  apply  the  pitch-board,  marking  the 


Fig.  33.    Method  of  Laying  Out  a  Simple,  Close-String  Stair. 

first  riser  about  9  inches  from  the  end ;  and  number  each  step  in  succes- 
sion. The  thickness  of  the  treads  and  risers  can  be  drawn  by  using 
thin  strips  of  hardwood  made  the  width  of  the  housing  required. 
Now  allow  for  the  wedges  under  the  treads  and  behind  the  risers,  and 
thus  find  the  exact  width  of  the  housing,  which  should  be  about  f  inch 


24  STAIR-BUILDING 

deep;  the  treads  and  risers  will  require  to  be  made  1}  inches  longer 
than  shown  in  the  plan,  to  allow  for  the  housings  at  both  ends. 

Before  putting  the  stair  together,  be  sure  that  it  can  be  taken 
into  the  house  and  put  in  position  without  trouble.  If  for  any  reason 
it  cannot  be  put  in  after  being  put  together,  then  the  parts  must  be 
assembled,  wedged,  and  glued  up  at  the  spot. 

It  is  essential  in  laying  out  a  plan  on  the  floor,  that  the  exact 
positions  of  the  first  and  last  risers  be  ascertained,  and  the  height  of 
the  story  wherein  the  stair  is  to  be  placed.  Then  draw  a  plan  of  the 
hall  or  other  room  in  which  the  stairs  will  be  located,  including  sur- 
rounding or  adjoining  parts  of  the  room  to  the  extent  of  ten  or  twelve 
feet  from  the  place  assigned  for  the  foot  of  the  stair.  All  the  door- 
ways, branching  passages,  or  windows  which  can  possibly  come  in 
contact  with  the  stair  from  its  commencement  to  its  expected  ter- 
mination or  landing,  must  be  noted.  The  sketch  must  necessarily  in- 
clude a  portion  of  the  entrance  hall  in  one  part,  and  of  the  lobby  or 
landing  in  another,  and  on  it  must  be  laid  out  all  the  lines  of  the 
stair  from  the  first  to  the  last  riser. 

The  height  of  the  story  must  next  be  exactly  determined  and 
taken  on  the  rod ;  then,  assuming  a  height  of  risers  suitable  to  the  place, 
a  trial  is  made  by  division  in  the  manner  previously  explained,  to 
ascertain  how  often  this  height  is  contained  in  the  height  of  the  story. 
The  quotient,  if  there  is  no  remainder,  will  be  the  number  of  risers 
required.  Should  there  be  a  remainder  on  the  first  division,  the  opera- 
tion is  reversed,  the  number  of  inches  in  the  height  being  made  the 
dividend  and  the  before-found  quotient  the  divisor;  and  the  operation 
of  reduction  by  division  is  carried  on  till  the  height  of  the  riser  is 
obtained  to  the  thirty-second  part  of  an  inch.  These  heights  are  then 
set  off  as  exactly  as  possible  on  the  story  rod,  as  shown  in  Fig.  33. 

The  next  operation  is  to  show  the  risers  on  the  sketch.  This 
the  workman  will  find  no  trouble  in  arranging,  and  no  arbitrary  rule 
can  be  given. 

A  part  of  the  foregoing  may  appear  to  be  repetition;  but  it  is  not, 
for  it  must  be  remembered  that  scarcely  any  two  flights  of  stairs  are 
alike  in  run,  rise,  or  pitch,  and  any  departure  in  any  one  dimension 
from  these  conditions  leads  to  a  new  series  of  dimensions  that  must 
be  dealt  with  independently.  The  principle  laid  down,  however, 
applies  to  all  straight  flights  of  stairs;  and  the  student  who  has  followed 


STAIR-BUILDING  25 

closely  and  retained  the  pith  of  what  has  been  said,  will,  if  he  has  a 
fair  knowledge  of  the  use  of  tools,  be  fairly  equipped  for  laying  out 
and  constructing  a  plain,  straight  stair  with  a  straight  rail. 

Plain  stairs  may  have  one  platform,  or  several;  and  they  may 
turn  to  the  right  or  to  the  left,  or,  rising  from  a  platform  or  landing, 
may  run  in  an  opposite  direction  from  their  starting  point. 

When  two  flights  are  necessary  for  a  story,  it  is  desirable  that 
each  flight  should  consist  of  the  same  number  of  steps;  but  this,  of 
course,  will  depend  on  the  form  of  the  staircase,  the  situation  and 
height  of  doors,  and  other  obstacles  to  be  passed  under  or  over,  as 
the  case  may  be. 

In  Fig.  32,  a  stair  is  shown  with  a  single  platform  or  landing  and 
three  newels.  The  first  part  of  this  stair  corresponds,  in  number  of 
risers,  with  the  stair  shown  in  Fig.  33;  the  second  newel  runs  down 
to  the  floor,  and  helps  to  sustain  the  landing.  This  newel  may  simply 
by  a  4  by  4-inch  post,  or  the  whole  space  may  be  inclosed  with  the 
spandrel  of  the  stair.  The  second  flight  starts  from  the  platform  just 
as  the  first  flight  starts  from  the  lower  floor,  and  both  flights  may  be 
attached  to  the  newels  in  the  manner  shown  in  Fig.  29.  The  bottom 
tread  in  Fig.  32  is  rounded  off  against  the  square  of  the  newel  post; 
but  this  cannot  well  be  if  the  stairs  start  from  the  landing,  as  the  tread 
would  project  too  far  onto  the  platform.  Sometimes,  in  high-class 
stairs,  provision  is  made  for  the  first  tread  to  project  well  onto  the 
landing. 

If  there  are  more  platforms  than  one,  the  principles  of  construc- 
tion will  be  the  same;  so  that  whenever  the  student  grasps  the  full 
conditions  governing  the  construction  of  a  single-platform  stair,  he 
will  be  prepared  to  lay  out  and  construct  the  body  of  any  stair  having 
one  or  more  landings.  The  method  of  laying  out,  making,  and  setting 
up  a  hand-rail  will  be  described  later. 

Stairs  formed  with  treads  each  of  equal  width  at  both  ends,  are 
named  straight  flights;  but  stairs  having  treads  wider  at  one  end  than 
the  other  are  known  by  various  names,  as  winding  stairs,  dog-legged 
stairs,  circular  stairs,  or  elliptical  stairs.  A  tread  with  parallel  sides, 
having  the  same  width  at  each  end,  is  called  a  fli/er;  while  one  having 
one  wide  end  and  one  narrow,  is  called  a  winder.  These  terms  will 
often  be  made  use  of  in  what  follows. 


26 


STAIR-BUILDING 


The  elevation  and  plan  of  the  stair  shown  in  Fig.  34  may  be 
called  a  dog-legged  stair  with  three  winders  and  six  flyers.  The  flyers, 
however,  may  be  extended  to  any  number.  The  housed  strings  to 
receive  the  winders  are  shown.  These  strings  show  exactly  the  manner 
of  construction.  The  shorter  string,  in  the  corner  from  1  to  4,  which 
is  shown  in  the  plan  to  contain  the  housing  of  the  first  winder  and 

half  of  the  second,  is  put 
up  first,  the  treads  being 
leveled  by  aid  of  a  spirit 
level ;  and  the  longer  upper 
string  is  put  in  place  after- 
wards, butting  snugly 
against  the  lower  string  in 
the  corner.  It  is  then 
fastened  firmly  to  the  wall. 
The  winders  are  cut  snugly 
around  the  newel  post,  and 
well  nailed.  Their  risers 
will  stand  one  above 
another  on  the  post;  and 
the  straight  string  above 
the  winders  will  enter  the 
post  on  a  line  with  the  top 
edge  of  the  uppermost 
winder. 

Platform  stairs  are  often 
constructed  so  that  one 
flight  will  run  in  a  direc- 
tion opposite  to  that  of  the 

other  flight,  as  shown  in  Fig.  35.  In  cases  of  this  kind,  the  landing  or 
platform  requires  to  have  a  length  more  than  double  that  of  the  treads, 
in  order  that  both  flights  may  have  the  same  width.  Sometimes, 
however,  and  for  various  reasons,  the  upper  flight  is  made  a  little 
narrower  than  the  lower;  but  this  expedient  should  be  avoided  when- 
ever possible,  as  its  adoption  unbalances  the  stairs.  In  the  example 
before  us,  eleven  treads,  not  including  the  landing,  run  in  one  direction ; 
while  four  treads,  including  the  landing,  run  in  the  opposite  direction ; 
or,  as  workmen  put  it,  the  stair  "returns  on  itself."  The  elevation 


Fig.  34.    Elevation  and  Plan  of   Dog-Legged   Stair 
with  Three  Winders  and  Six  Flyers. 


STAIR-BUILDING 


27 


1 

1 

\ 

1 

1 

1 

I2| 

ii 

10 

9 

Q 

7 

6 

5 

1 

3 

2 

\ 

Lar»dinq      | 

B 

j 

'                                                   | 

Newel 

13 

14 

!5 

16 

Wa.ll 

Fig.  85.    Plan  of  Platform  Stair  Returning  on  Itself. 

shown  in  Fig.  36  illustrates  the  manner  in  which  the  work  is  executed. 
The  various  parts  are  shown  as  follows: 

Fig.  37  is  a  section  of  the  top  landing,  with  baluster  and  rail. 

Fig.  38  is  part  of  the  long  newel,  showing  mortises  for  the  strings. 


Fig.  36.    Elevation  Showing  Construction  of  Platform  Stair  of  which  Plau  is 
Uiven  in  Fig.  35. 


STAIR-BUILDING 


ofFTo  37Landin°n 
Baiuster.andRaii'. 


Fig.  39  represents  part  of  the  bottom  newel,  showing  the  string, 
moulding  on  the  outside,  and  cap. 

Fig.  40  is  a  section  of  the  top  string  enlarged. 

Fig.  41  is  the  newel  at  the  bottom,  as  cut  out  to 
receive  bottom  step.  It  must  be  remembered  that 
there  is  a  cove  under  each  tread.  This  may  be  nailed 
in  after  the  stairs  are  put  together,  and  it  adds  greatly 
to  the  appearance. 

We  may  state  that  stairs  should  have  carriage  pieces 
fixed  from  floor  to  floor,  under  the  stairs,  to  support 
them.  These  may  be  notched  under  the  steps;  or 
rough  brackets  may  be  nailed  to  the  side  of  the  car- 
riage, and  carried  under  each  riser  and  tread. 

There  is  also  a  framed  spandrel  which  helps  materially  to  carry 
the  weight,  makes  a  sound  job,  and 
adds  greatly  to  the  appearance.  This 
spandrel  may  be  made  of  IJ-inch 
material,  with  panels  and  mouldings 
on  the  front  side,  as  shown  in  Fig.  36. 
The  joint  between  the  top  and  bottom 
rails  of  the  spandrel  at  the  angle, 
should  be  made  as  shown  in  Fig.  42 
with  a  cross-tongue,  and  glued  and 
fastened  with  long  screws.  Fig.  43  is 
simply  one  of  the  panels  showing  the 
miters  on  the  moulding  and  the  shape 
of  the  sections.  As  there  is  a  conven- 
ient space  under  the  landing,  it  is  commonly  used  for  a  closet. 

In  setting  out  stairs,  not  only  the  proportions  of  treads  and  risers 
must  be  considered,  but  also  the  material  available. 
As  this  material  runs,  as  a  rule,  in  certain  sizes,  it  is 
best  to  work  so  as  to  conform  to  it  as  nearly  as 
possible.     In  ordinary  stairs,  11  by  1-inch  common 
stock  is  used  for  strings  and  treads,  and  7-inch  by 
f-inch  stock  for  risers;  in  stairs  of  a  better  class, 
Fig.  40.  Eniarg-     wider  and  thicker  material  may  be  used.    The  rails 
^section  of  TOP     are  set  ^  various  heights;  2  feet  8  inches  may  be 


Fig.  38.  String 
Mortises  in  Long 
Newel. 


Fig.  39.  Mortises 
In  Lower  Newel 
for  String,  Out- 
side Mo  ulding,  and 
Cap. 


STAIR-BUILDING 


29 


taken  as  an  average  height  on  the  stairs,  and  3  feet  1  inch  on  landings, 
with  two  balusters  to  each  step. 

In  Fig.  36,  all  the  newels  and  balusters  are  shown  square;  but 
it  is  much  better,  and  is  the  more  common  practice,  to  have  them 


I 


Newel 


Fig.  41.  K 
to  Receive 
Step. 


41.    Newel  Cut 
Bottom 


5V; 


Fig.  42.  Showing  Method  of  Joining 
taudrel  Rails,  with  Cross-Tongue 
m-d  and  Screwed. 


turned,  as  this  gives  the  stairs  a  much  more  artistic  appearance. 
The  spandrel  under  the  string  of  the  stairway  shows  a  style  in  which 
many  stairs  are  finished  in  hallways  and  other  similar  places.  Plaster 
is  sometimes  used  instead  of  the  panel  wrork,  but  is  not  nearly  so  good 
as  woodwork.  The  door  under  the  landing  may  open  into  a  closet, 
or  may  lead  to  a  cellarway,  or  through  to  some  other  room. 

In  stairs  with  winders,  the  width  of  a  winder  should,  if  possible, 
be  nearly  the  width  of  the  regular  tread,  at 
a  distance  of  14  inches  from  the  narrow 
end,  so  that  the  length  of  the  step  in 
walking  up  or  down  the  stairs  may  not 
be  interrupted;  and  for  this  reason  and 
several  others,  it  is  always  best  to  have  M 
three  winders  only  in  each  quarter-turn. 
Above  all,  avoid  a  four-winder  turn,  as 
this  makes  a  breakneck  stair,  which  is 
more  difficult  to  construct  and  incon- 
venient to  use. 

Bullnose  Tread.  No  other  stair,  perhaps,  looks  so  well  at  the 
starting  point  as  one  having  a  buhnose  step.  In  Fig.  44  are  shown  a 
plan  and  elevation  of  a  flight  of  stairs  having  a  bullnose  tread.  The 
method  of  obtaining  the  lines  and  setting  out  the  body  of  the  stairs, 


Fig.  43.  Panel  in  Spandrel,  Show 

ing  Mi  UTS  on  Moulding,  and 

Shape  of  Section. 


30 


STAIR-BUILDING 


is  the  same  as  has  already  been  explained  for  other  stairs,  with  the 
exception  of  the  first  two  steps,  which  are  made  with  circular  ends, 
as  shown  in  the  plan.  These  circular  ends  are  worked  out  as  here- 
after described,  and  are  attached  to  the  newel  and  string  as  shown. 


Scale  of£i 


I 


Fig.  44.    Elevation  and  Plan  of  Stair  with  Bullnose  Tread. 

The  example  shows  an  open,  cut  string  with  brackets.  The  spandrel 
under  the  string  contains  short  panels,  and  makes  a  very  handsome 
finish.  The  newels  and  balusters  in  this  case  are  turned,  and  the  latter 
have  cutwork  panels  between  them. 


STAIR-BUILDING 


Fig.  45.  Section 
through  Bullnose 
Step. 


Bullnose  steps  are  usually  built  up  with  a  three- 
piece  block,  as  shown  in  Fig.  45,  which  is  a  sec- 
tion through  the  step  indicating  the  blocks,  tread, 
and  riser. 

Fig.  46  is  a  plan  showing  how  the  veneer  of  the 
riser  is  prepared  before  being  bent  into  position.  The  block  A  indi- 
cates a  wedge  which  is  glued  and  driven  home  after  the  veneer  is 
put  in  place.  This  tightens  up  the  work  and  makes  it  sound  and 
clear.  Figs.  47  and  48  show  other  methods  of  forming  bullnose  steps. 
Fig.  49  is  the  side  elevation  of  an  open-string  stair  with  bullnose 
steps  at  the  bottom; 
while  Fig.  50  is  a  view 
showing  the  lower  end 
of  the  string,  and  the 
manner  in  which  it  is 
prepared  for  fixing  to 
the  blocks  of  the  step. 
Fig.  5L  is  a  section 
through  the  string,  showing  the  bracket,  cove,  and  projection  of  tread 
over  same. 

Figs.  52  and  53  show  respectively  a  plan  and  vertical  section  of 
the  bottom  part  of  the  stair.  The  blocks  are  shown  at  the  er>.ls  of  the 
steps  (Fig.  53),  with  the  veneered  parts  of  the  risers  going  round  them; 
also  the  position  where  the  string  is  fixed  to  the  blocks  (Fig.  52);  and 


Newel 


Fig.  46.    Plan  Showing  Preparation  of  Veneer  before 
Bending  into  Position. 


Fig.  47. 


Fig.  48. 


Methods  of  Forming  Bulluose  Steps. 


the  tenon  of  the  newel  is  marked  on  the  upper  step.  The  section  (Fig. 
53)  shows  the  manner  in  which  the  blocks  are  built  up  and  the  newel 
tenoned  into  them. 


32 


STAIR-BUILDING 


Pig.  49.    Side  Elevation  of  Open-String 
Stair  with  Bullnose  Steps. 


The  newel,  Fig.  49,  is  rather  an 
elaborate  affair,  being  carved  at  the 
base  and  oa  the  body,  and  having 
a  carved  rosette  planted  in  a  small, 
sunken  panel  on  three  sides,  the  rail 
butting  against  the  fourth  side. 

Open-Newel  Stairs.  Before  leav- 
ing the  subject  of  straight  and  dog- 
legged  stairs,  the  student  should  be 
made  familiar  with  at  least  one 
example  of  an  open-newel  stair.  As 
the  same  principles  of  construction 
govern  all  styles  of  open-newel 

stairs,  a  single  example  will  be  sufficient.     The  student  must,  of 
course,  understand  that  he  himself  is  the  greatest  factor  in  planning 
stairs  of  this  type;  that  the  setting  out  and  design- 
ing will  generally  devolve  on  him.    By  exercising 
a  little  thought  and  foresight,  he  can  so  arrange 
his  plan  that  a  minimum  of  both  labor  and  material 
will  be  required. 

Fig.  54  shows  a  plan  of  an  open-newel  stair 

having  t  vo  landings  and  closed  strings,  shown  in 

elevation  in  Fig.  55.    The  dotted  lines  show  the 

carriage  timbers  and  trimmers,  also  the  lines  of 

risers;  while  the  treads  are  shown  by  full  lines. 

It  will  be  noticed  that  the  strings  and  trimmers 

at  the  first  landing  are  framed  into  the  shank  of  the  second  newel 

post,  which  runs  down  to  the  floor;  while  the  top  newel  drops  below 
the  fascia,  and  has  a  turned  and  carved  drop.  This  drop 
hangs  below  both  the  fascia  and  the  string.  The  lines 
of  treads  and  risers  are  shown  by  dotted  lines  and 
crosshatched  sections.  The  position  of  the  carriage 
timbers  is  shown  both  in  the  landings  and  in  the  runs 
Fig.  51.  section  of  the  stairs,  the  projecting  ends  of  these  timbers  being 

through  String.  .          .  .  ,  11        »          i        i>    i          i 

supposed  to  be  resting  on  the  wall.  A  scale  ot  the  plan 
and  elevation  is  attached  to  the  plan.  In  Fig.  55,  a  story  rod  is 
shown  at  the  right,  with  the  number  of  risers  spaced  off  thereon. 
The  design  of  the  newels,  spandrel,  framing,  and  paneling  is  shown. 


Fig.  50.  Lower  End 
of  String  to  Connect 
with  Bullnose  Step. 


STAIR-BUILDING 


Fig.  53.    Plan  of  Bottom  Part 
of  Bullnose  Stair 


Fig.  53,    Vertical  Section  through 
Bottom  Part  of  Bullnose  Stair. 


Only  the  central  carriage  timbers  are  shown  in  Fig.  54;  but  in  a 
stair  of  this  width,  there  ought  to  be  two  other  timbers,  not  so  heavy, 
perhaps,  as  the  central  one,  yet  strong  enough  to  be  of  service  in  lend- 
ing additional  strength  to  the  stairway,  and  also  to  help  carry  the  laths 
and  plaster  or  the  paneling  which  may  be  necessary  in  completing 
the  under  side  or  soffit.  The  strings  being  closed,  the  butts  of  their 
balusters  must  rest  on  a  subrail  which  caps  the  upper  edge  of  the 
outer  string. 

n 


-    ----- 


.t.ii 

m 

ci!| 


I! 


Well  -Hole 


|£|j 


67  Feet 


Fig.  54.    Plan  of  Open-Newel  Stair,  with  Two  Landings  and  Closed  Strings. 


34 


STAIR-BUILDING 


The  first  newel  should  pass  through  the  lower  floor,  and,  to 
insure  solidity,  should  be  secured  by  bolts  to  a  joist,  as  shown  in  the 
elevation.  The  rail  is  attached  to  the  newels  in  the  usual  manner, 
with  handrail  bolts  or  other  suitable  device.  The  upper  newel  should 
be  made  fast  to  the  joists  as  shown,  either  by  bolts  or  in  some  other 


qn 

Fig.  55.    Elevation  of  Open-Newel  Stair  Shown  in  Plan  in  Fig. 

efficient  manner.  The  intermediate  newels  are  left  square  on  the 
shank  below  the  stairs,  and  may  be  fastened  in  the  floor  below  either 
by  mortise  and  tenon  or  by  making  use  of  joint  bolts. 

Everything  about  a  stair  should  be  made  solid  and  sound;  and 
every  joint  should  set  firmly  and  closely;  or  a  shaky,  rickety,  squeaky 
stair  will  be  the  result,  which  is  an  abomination. 

Stairs  with  Curved  Turns.  Sufficient  examples  of  stairs  having 
angles  of  greater  or  less  degree  at  the  turn  or  change  of  direction,  to 


STAIR-BUILDING 


35 


enable  the  student  to  build  any  stair  of  this  class,  have  now  been 
given.  There  are,  however,  other  types  of  stairs  in  common  use, 
whose  turns  are  curved,  and  in  which  newels  are  employed  only  at 
the  foot,  and  sometimes  at  the  finish  of  the  flight.  These  curved  turns 
may  be  any  part  of  a  circle,  according  to  the  requirements  of  the  case, 
but  turns  of  a  quarter-circle  or  half-circle  are  the  more  common. 
The  string  forming  the  curve  is  called  a  cylinder,  or  part  of  a  cylinder, 
as  the  case  may  be.  The  radius  of  this  circle  or  cylinder  may  be  any 
length,  according  to  the  space  assigned  for  the  stair.  The  opening 
around  which  the  stair  winds  is  called  the  well-hole. 

Fig.  56  shows  a  portion  of  a  stairway  having  a  well-hole  with 
a  7-inch  radius.  This  stair  is  rather  peculiar,  as  it  shows  a  quarter- 
space  landing,  and  a  quarter-space  having 
three  winders.  The  reason  for  this  is  the 
fact  that  the  landing  is  on  a  level  with  the 
floor  of  another  room,  into  which  a  door 
opens  from  the  landing.  This  is  a  problem 
very  often  met  with  in  practical  work, 
where  the  main  stair  is  often  made  to  do 
the  work  of  two  flights  because  of  one  floor 
being  so  much  lower  than  another. 

A  curved  stair,  sometimes  called  a 
geometrical  stair,  is  shown  in  Fig.  57, 
containing  seven  winders  in  the  cylinder 
or  well -hole,  the  first  and  last  aligning  with  the  diameter. 

In  Fig.  58  is  shown  another  example  of  this  kind  of  stair,  con- 
taining nine  winders  in  the  well-hole,  with  a  circular  wall-string. 
It  is  not  often  that  stairs  are  built  in  this  fashion,  as  most  stairs  having 
a  circular  well-hole  finish  against  the  wall  in  a  manner  similar  to  that 
shown  in  Fig.  57. 

Sometimes,  however,  the  workman  will  be  confronted  with  a 
plan  such  as  shown  in  Fig.  58;  and  he  should  know  how  to  lay  out 
the  wall-string.  In  the  elevation,  Fig.  58,  the  string  is  shown  to  be 
straight,  similar  to  the  string  of  a  common  straight  flight.  This  results 
from  having  an  equal  width  in  the  winders  along  the  wall-string,  and, 
as  we  have  of  necessity  an  equal  width  in  the  risers,  the  development 
of  the  string  is  merely  a  straight  piece  of  board,  as  in  an  ordinary 
straight  flight.  In  laying  out  the  string,  all  we  have  to  do  is  to  make 


Fig.  56. 

Flights,  with  Mid-Floor 


Stair  Serving  for  Two 
,  with  Mic 
Landing. 


36 


STAIR-BUILDING 


a  common  pitch-board,  and,  with  it  as  a  templet,  mark  the  lines  of 
the  treads  and  risers  on  a  straight  piece  of  board,  as  shown  at  1,  2,  3, 
4,  etc. 

If  you  can  manage  to  bend  the  string  without  kerfing  (grooving), 
it  will  be  all  the  better;  if  not,  the  kerfs  (grooves)  must  be  parallel  to 
the  rise.    You  can  set  out  with  a  straight  edge,  full  size,  on  a  rough 
platform,  just  as  shown  in  the  diagram;  and 
when  the  string  is  bent  and  set  in  place,  the 
risers  and    winders    will    have    their  correct 
positions. 

To  bend  these  strings  or  otherwise  prepare 
them  for  fastening  against  the  wall,  perhaps 
the  easiest  way  is  to  saw  the  string  with  a  fine 
saw,  across  the  face,  making  parallel  grooves. 
This  method  of  bending  is  called  kerfing, 
above  referred  to.  The  kerfs  or  grooves 

must  be  cut  parallel  to  the  lines  of  the  risers,  so  as  to  be  vertical  when 
the  string  is  in  place.  This  method,  however — handy  though  it  may 
be — is  not  a  good  one,  inasmuch  as  the  saw  groove  will  show  more  or 
less  in  the  finished  work. 

Another  method  is  to  build  up  or  stave  the  string.    There  are 


Fig.  57.    Geometrical  Stair 
with  Seven  Winders. 


Fig.  58.    Plan  of  Circular  Stair  and  Layout  of  Wall  String 
for  Same. 


several  ways  of  doing  this.  In  one,  comparatively  narrow  pieces  are 
cut  to  the  required  curve  or  to  portions  of  it,  and  are  fastened  together, 
edge  to  edge,  with  glue  and  screws,  until  the  necessary  width  is 
obtained  (see  Fig.  59).  The  heading  joints  may  be  either  butted  or 
beveled,  the  latter  being  stronger,  and  should  be  cross-tongued. 

Fig.  60  shows  a  method  that  may  be  followed  when  a  wide  string 
is  required,  or  a  piece  curbed  in  the  direction  of  its  width  is  needed 


STAIR-BUILDING 


37 


for  any  purpose.  The  pieces  are  stepped  over  each  other  to  suit  the 
desired  curve;  and  though  shown  square-edged  in  the  figure,  they  are 
usually  cut  beveled,  as  then,  by  reversing  them,  two  may  be  cut  out 
of  a  batten. 

Panels  and  quick  sweeps  for  similar  purposes  are  obtained  in  the 
manner  shown  in  Fig.  Gl,  by  joining  up  narrow  boards  edge  to  edge 


Fig.  59. 


Methods  of  Building  Up  Strings. 


Fig.  60. 


at  a  suitable  bevel  to  give  the  desired  curve.  The  internal  curve  is 
frequently  worked  approximately,  before  gluing  up.  The  numerous 
joints  incidental  to  these  methods  limit  their  uses  to  painted  or  unim- 
portant work. 

In  Fig.  62  is  shown  a  wreath-piece  or  curved  portion  of  the 
outside  string  rising  around  the  cylinder  at  the  half-space. 
This  is  formed  by  reducing  a  short  piece  of  string  to  a  veneer 
between  the  springings;  bending  it  upon  a  cylinder  made  to  fit  the 
plan;  then,  when  it  is  secured  in  position,  filling  up  the  back  of  the 
veneer  with  staves  glued  across  it;  and,  finally,  gluing  a  piece  of  canvas 
over  the  whole.  The  appearance  of  the 
wreath-pi  ce  after  it  has  been  built  up  and 
removed  Lx>m  the  cylinder  is  indicated  in 
Fig.  63.  The  canvas  back  has  been  omitted 
to  show  the  staving;  and  the  counter-wedge 
key  used  for  connecting  the  wreath-piece 
with  the  string  is  shown.  The  wreath- 
piece  is,  at  this  stage,  ready  for  marking 
the  outlines  of  the  steps. 

Fig.  62  also  shows  the  drum  or  shape  around  which  strings  may 
be  bent,  whether  the  strings  are  formed  of  veneers,  staved,  or  kerfed. 
Another  drum  or  shape  is  shown  in  Fig.  64.  In  this,  a  portion  of  a 
cylinder  is  formed  in  the  manner  clearly  indicated;  and  the  string, 
Ixiiug  set  out  on  a  veneer  board  sufficiently  thin  to  bend  easily,  is  laid 


Fig.  61.    Building  Up  a  Curved 
Panel  or  Quick  Sweep. 


38 


STAIR-BUILDING 


down  round  the  curve,  such  a  number  of  pieces  of  like  thickness  being 
then  added  as  will  make  the  required  thickness  of  the  string.  In 
working  this  method,  glue  is  introduced  between  the  veneers,  which 


Pig.  62.    Wreath- 
Piece  Bent 
around  Cylinder. 


Fig.  63.  CompletedWreath- 
Piecp  Removed  from 
Cylinder. 


64.    Another  Drum  or 
shape   for    Building 
Curved  Strings. 


are  then  quickly  strained  down  to  the  curved  piece  with  hand  screws. 
A  string  of  almost  any  length  can  be  formed  in  this  way,  by  gluing 
a  few  feet  at  a  time,  and  when  that  dries,  removing  the  cylindrical 
curve  and  gluing  down  more,  until  the  whole  is  completed.  Several 
other  methods  will  suggest  themselves  to  the  workman,  of  building  up 
good,  solid,  circular  strings. 

One  method  of  laying  out  the  treads  and  risers  around  a  cylinder 
or  drum,  is  shown  in  Fig.  65.  The  line  D  shows  the  curve  of  the  rail. 
The  lines  showing  treads  and  risers  may  be  marked  off  on  the  cylinder, 
or  they  may  be  marked  off  after  the  veneer  is  bent  around  the  drum  or 
cylinder. 

There  are  various  methods  of  making  inside  cylinders  or  wells, 
and  of  fastening  same  to  strings.  One  method  is  shown  in  Fig.  66. 
This  gives  a  strong  joint  when  properly  made.  It  will  be  noticed  that 
the  cylinder  is  notched  out  on  the  back;  the  two  blocks  shown  at  the 
back  of  the  offsets  are  wedges  driven  in  to  secure  the  cylinder  in  place, 
and  to  drive  it  up  tight  to  the  strings.  Fig.  67  shows  an  8-inch  well- 
hole  with  cylinder  complete;  also  the  method  of  trimming  and  finish- 
ing same.  The  cylinder,  too,  is  shown  in  such  a  manner  that  its  con- 
struction will  be  readily  understood. 

Stairs  having  a  cylindrical  or  circular  opening  always  require 
a  weight  support  underneath  them.  This  support,  which  is  generally 
made  of  rough  lumber,  is  called  the  carriage,  because  it  is  supposed 


STAIR-BUILDING 


39 


to  carry  any  reasonable  load  that  may  be  placed  upon  the  stairway. 
Fig.  68  shows  the  under  side  of  a  half-space  stair  having  a  carriage 
beneath  it.    The  timbers  marked  S  are  of  rough  stuff,  and  may  be 
2-inch  by  6-inch  or  of  greater  dimensions.    If  they 
are  cut  to  fit  the  risers  and  treads,  they  will  require 
to  be  at  least  2-inch  by  8-inch. 

In  preparing  the  rough  carriage  for  the 
winders,  it  will  be  best  to  let  the  back  edge  of  the 
tread  project  beyond  the  back  of  the  riser  so  that  it 
forms  a  ledge  as  shown  under  C  in  Fig.  69.  Then 
fix  the  cross-carriage  pieces  under  the  winders, 
with  the  back  edge  about  flush  with  the  backs 
of  risers,  securing  one  end  to  the  well  with  screws, 
and  the  other  to  the  wall  string  or  the  wall.  Now 
cut  short  pieces,  marked  0  0  (Fig.  68),  and  fix  them  tightly  in  between 
the  cross-carriage  and  the  back  of  the  riser  as  at  B  B  in  the  section, 
Fig.  69.  These  carriages  should  be  of  3-inch  by  2-inch  material. 
Now  get  a  piece  of  wood,  1-inch  by  3-inch,  and  cut  pieces  C  C  to  fit 
tightly  between  the  top  back  edge  of  the  winders  (or  the  ledge)  and 
the  pieces  marked  B  B  in  section.  This  method  makes  a  very 
sound  and  strong  job  of  the  winders;  and  if  the  stuff  is  roughly 
planed,  and  blocks  are  glued  on  each  side  of  the  short  cross-pieces 
000,  it  is  next  to  impossible  for  the  winders  ever  to  spring  or 
squeak.  When  the  weight  is  carried  in  this  manner,  the  plasterer  will 


Fig.  65.  La 
Treads  and 
around  a  Drum. 


lying  Out 
Treads  and  Risers 


Fig.  66.    One  Method 

of  Making  an  Inside 

Well. 


Fig.  67.    Construction  and 

Trimming  of  8-Inch 

Well-Hole. 


have  very  little  trouble  in  lathing  so  that  a  graceful  soffit  will  be  made 
under  the  stairs. 

The  manner  of  placing  the  main  stringers  of  the  carriage  S  S, 
is  shown  r.t  A,  Fig.  69.    Fig.  68  shows  a  complete  half-space  stair; 


40 


STAIR-BUILDING 


one-half  of  this,  finished  as  shown,  will  answer  well  for  a  quarter-space 
stair. 

Another  method  of  forming  a  carriage  for  a  stair  is  shown  in 
Fig.  70.  This  is  a  peculiar  but  very  handsome  stair,  inasmuch  as  the 
first  and  the  last  four  steps  are  parallel,  but  the  remainder  balance  or 
dance.  The  treads  are  numbered  in  this  illustration;  and  the  plan  of 

the  handrail  is  shown  ex- 
tending from  the  scroll  at 
the  bottom  of  the  stairs  to 
the  landing  on  the  second 
Stoi7-  The  trimmer  T  at 
the  top  of  the  stairs  is  also 
shown ;  and  the  rough  strings 
or  carriages,  RS,RS,RS, 
are  represented  by  dotted 
lines. 

This  plan  represents  a 
stair  with  a  curtail  step, 
and  a  scroll  handrail  rest- 
ing over  the  curve  of  the 
curtail  step.  This  type  of 
stair  is  not  now  much  in 
vogue  in  this  country, 
though  it  is  adopted  occa- 
sionally in  some  of  the  larger  cities.  The  use  of  heavy  newel  posts 
instead  of  curtail  steps,  is  the  prevailing  style  at  present. 

In  laying  out  geometrical  stairs,  the  steps  are  arranged  on  prin- 
ciples already  described.  The  well-hole  in  the  center  is  first  laid  down 
and  the  steps  arranged  around  it.  In  circular  stairs  with  an  open  well- 
hole,  the  handrail  being  on  the  inner  side,  the  width  of  tread  for  the 
steps  should  be  set  off  at  about  18  inches  from  the  handrail,  this 
giving  an  approximately  uniform  rate  of  progress  for  anyone  ascending 
or  descending  the  stairway.  In  stairs  with  the  rail  on  the  outside,  as 
sometimes  occurs,  it  will  be  sufficient  if  the  treads  have  the  proper 
width  at  the  middle  point  of  their  length. 

Where  a  flight  of  stairs  will  likely  be  subject  to  great  stress  and 
wear,  the  carriages  should  be  made  much  heavier  than  indicated  in 


Fig.  68.    Under  Side  of  Half-Space  Stair,  with 
Carriages  and  Cross-Carriages. 


STAIR-BUILDING 


41 


Fig.  69.    Method  of  Reinforcing  Stair. 


the  foregoing  figures;  and  there  may  be  cases  when  it  will  be  necessary 
to  use  iron  bolts  in  the  sides  of  the  rough  strings  in  order  to  give  them 
greater  strength.  This  necessity,  however,  will  arise  only  in  the  case 

of  stairs  built  in  public  buildings, 
churches,  halls,  factories,  ware- 
houses, or  other  buildings  of  a  simi- 
lar kind.  Sometimes,  even  in  house 
stairs  it  may  be  wise  to  strengthen 
the  treads  and  risers  by  spiking 
pieces  of  board  to  the  rough  string, 
ends  up,  fitting  them  snugly  against 
the  under  side  of  the  tread  and  the 
back  of  the  riser.  The  method  of  doing  this  is  shown  in  Fig.  71,  in 
which  the  letter  0  shows  the  pieces  nailed  to  the  string. 

Types  of  Stairs  in  Common  Use.  In  order  to  make  the  student 
familiar  with  types  of  stairs  in  general  use  at  the  present  day,  plans 
of  a  few  of  those  most  likely 
to  be  met  with  will  now  be 
given. 

Fig.  72  is  a  plan  of  a 
straight  stair,  with  an  ordi- 
nary cylinder  at  the  top 
provided  for  a  return  rail 
on  the  landing.  It  also 
shows  a  stretch-out  stringer 
at  the  starting. 

Fig.  73  is  a  plan  of  a 
stair  with  a  landing  and 
return  steps. 

Fig.  74  is  a  plan  of  a 
stair  with  an  acute  angular 
landing  and  cylinder. 

Fig.    75  illustrates  the 
same  kind  of  stair  as  Fig.  74,  the   angle,  however,    being   obtuse. 
Fig.  76  exhibits  a  stair  having  a  half-turn  with  two  risers  on  land- 
ings. 

Fig.  77  is  a  plan  of  a  quarter-space  stair  with  four  winders. 
Fig.  78  shows  a  stair  similar  to  Fig.  77,  but  with  six  winders. 


Fig.  70.  Plan  Showing  One  Method  of  Constructing 
Carriage  and  Trimming  Winding  Stair. 


42 


STAIR-BUILDING 


Pig.  71.    Reinforcing  Treads  and  Risers 
by  Blocks  Nailed  to  String. 


Fig.  72.     Plan  of  Straight  Stair  with 
Cylinder  at  Top  for  Return  Rail. 

Fig.  79  shows  a  stair  having  five 
dancing  winders. 

Fig.  80  is  a  plan  of  a  half-space 
stair  having  five  dancing  winders 
and  a  quarter-space  landing. 
Fig.  81  shows  a  half-space  stair  with  dancing  winders  all  around 
the  cylinder. 

Fig.  82  shows  a  geometrical  stair  having 
winders  all  around  the  cylinder. 

Fig.  83  shows  the  plan  and  elevation  of 
stairs  which  turn  around  a  central  post.  This 
kind  of  stair  is  frequently  used  in  large  stores 
and  in  clubhouses  and  other  similar  places, 
and  has  a  very  graceful  appearance.  It  is  not 
very  difficult  to  build  if  properly  planned. 

The  only  form  of  stair  not  shown  which  the 
student  may  be  called  upon  to  build,  would 
very  likely  be  one  having  an  elliptical  plan; 
but,  as  this  form  is  so  seldom  used — being 
found,  in  fact,  only  in  public  buildings  or 
great  mansions — it  rarely  falls  to  the  lot  of 
the  ordinary  workman  to  be  called  upon  to  design  or  construct  a 
stairway  of  this  type. 


Fig.  73.    Plan  of  Stair  with 
Landing  and  Return  Steps. 


Fig.  74.  Plan  of  Stair  with  Acute- Angle 
Landing  and  Cylinder. 


Fig.  75.  Plan  of  Stair  with  Obtuse- Angle 
Landing  and  Cylinder. 


STAIR-BUILDING 


43 


Fig.  77.     Quarter-Space  Stair  with 
Four  Winders. 


Fig.  76.  Half-Turn  Stair  with 
Two  Risers  on  Landings. 


Fig.  78.    Quarter-Space  Stair  with  Six 
Winders. 


Fig.  81.    Half-Space  Stair  with 

Dancing     Winders      all 

around  Cylinder. 


GEOMETRICAL    STAIRWAYS   AND 
HANDRAILING 

The  term  geometrical  is  applied  to  stair- 
ways having  any  kind  of  curve  for  a  plan. 
The  rails  over  the  steps  are  made  con- 
tinuous  from   one   story   to    another.      The    resulting    winding  01 
twisting  pieces  are  called  wreaths. 

Wreaths.  The  construction  of  wreaths  is  based  on  a  few 
geometrical  problems — namely,  the  projection  of  straight  and  curved 
lines  into  an  oblique  plane;  and  the  finding  of  the  ingle  of  inclination 
of  the  plane  into  which  the  linos  and  curves  arc  projected.  This  angle 


Fig.  80.    Half-Space  Stair  with 

Five  Dancing  Winders  and 

Quarter-Space  Landing. 


44 


STAIR-BUILDING 


Fig.  83.     Plan  and  Eleva- 
tion of  Stairs  Turning 
around  a  Central 
Post. 


Fig.  82.  Geometrical  Stair  with 
Winders  all  Around  Cylinder. 

is  called  the  bevel,    and    by    its    use 
the    wreath  is  made  to  twist. 

In  Fig.  84  is  shown  an  obtuse- 
angle  plan;  in  Fig.  85,  an  acute-angle 
plan :  and  in  Fig.  86,  a  semicircle  en- 
closed within  straight  lines. 

Projection.  A  knowledge  of  how 
to  project  the  lines  and  curves  in  each 
of  these  plans  into  an  oblique  plane, 
and  to  find  the  angle  of  inclination  of 
the  plane,  will  enable  the  student  to 
construct  any  and  all  kinds  of  wreaths. 

The  straight  lines  a,  b,  c,  d  in  the  plan,  Fig.  86,  are  known  as 
tangents;  and  the  curve,  the  central  line  of  the  plan  wreath. 

The  straight  line  across  from  n  to  n  is  the  diameter;  and  the 
perpendicular  line  from  it  to  the  lines  c  and  b  is  the  radius. 

A  tangent  line  may  be  defined  as  a  line  touching  a  curve  without 
cutting  it,  and  is  made  use  of  in  handrailing  to  square  the  joints  of  the 
wreaths. 

Tangent  System.  The  tangent  system  of  handrailing  takes  its 
name  from  the  use  made  of  the  tangents  for  this  purpose. 

In  Fig.  86,  it  is  shown  that  the  joints  connecting  the  central  line 
of  rail  with  the  plan  rails  w  of  the  straight  flights,  are  placed  right  at 
the  springing;  that  is,  they  are  in  line  with  the  diameter  of  the  semi- 
circle, and  square  to  the  side  tangents  a  and  d. 

The  center  joint  of  the  crown  tangents  is  shown  to  be  square  to 
tangents  b  and  c.  When  these  lines  are  projected  into  an  oblique 
plane,  the  joints  of  the  wreaths  can  be  made  to  butt  square  by  applying 
the  bevel  to  them. 


STAIR-BUILDING 


4.5 


Fig.  84.    Obtuse-  Angle  Plan. 


Joint 


All  handrail  wreaths  are  assumed  to  rest  on  an  oblique  plane 

while  ascending  around  a  well-hole,  either  in  connecting  two  flights 

or  in  connecting  one  flight  to  a 

landing,  as  the  case  may  be. 
In   the  simplest   cases  of 

construction,  the  wreath  rests 

on  an  inclined  plane  that  in- 

clines in  one  direction  only,  to 

either  side  of  the  well-hole;  while  in  other  cases  it  rests  on  a  plane 

that  inclines  to  two  sides. 

Fig.  87  illustrates  what  is  meant  by  a  plane  inclining  in  one 

direction.  It  will  be  noticed 
that  the  lower  part  of  the  figure 
is  a  reproduction  of  the  quad- 
rant enclosed  by  the  tangents 
a  and  b  in  Fig.  86.  The 
quadrant,  Fig.  87,  represents  a 
central  line  of  a  wreath  that  is 
to  ascend  from  the  joint  on  the 
plan  tangent  a  the  height  of  h 
above  the  tangent  b. 
rig.  ss.  Acute-  Angle  Plan.  In  Fig.  88,  a  view  of  Fig.  87 

is  given  in  which  the  tangents  a 

and  b  are  shown  in  plan,  and  also  the  quadrant  representing  the  plan 

central  line  of  a  wreath.    The  curved  line  extending  from  a  to  h  in 

this  figure  represents  the  development  of  the  central  line  of  the  plan 

wreath,  and,  as  shown,  it  rests  on  an  oblique  plane  inclining  to  one 

side  only  —  namely,  to  the  side  of 

the  plan  tangent  a.    The  joints 

are  made  square  to  the  devel- 

oped tangents  a  and  m  of  the  in- 

clined   plane;    it    is     for    this 

purpose  only  that  tangents  are 

made  use  of  in  wreath  construc- 

tion.   They   are   shown   in   the 

figure  to  consist  of   two  lines, 

a  and  m,  which  are  two  adjoining 

sides  of  a  developed  section  (in 


Fig. 


Semicircular  Plan. 


46 


STAIR-BUILDING 


illustrating  plane 

inclined    in^One  Directioa 


this  case,  of  a  square  prism),  the  section  being  the  assumed  inclined 
plane  whereon  the  wreath  rests  in  its  ascent  from  a  to  h.    The  joiiit  at  h, 
if  made  square  to  the  tangent  ra,  will  be  a  true,  square  butt-joint;  so 
also  will  be  the  joint  at  a,  if  made  square  to 
the  tangent  a. 

In  practical  work  it  will  be  required  to  find 
the  correct  goemetrical  angle  between  the  two 
developed  tangents  a  and  ra;  and  here,  again, 
it  may  be  observed  that  the  finding  of  the 
Joint  correct  angle  between  the  two  developed 
tangents  is  the  essential  purpose  of  every 
tangent  system  of  handrailing. 

In  Fig.  89  is  shown  the  geometrical  solu- 
tion —  the  one  necessary  to  find  the  angle 
between  the  tangents  as  required  on  the  face- 
mould  to  square  the  joints  of  the  wreath. 

The  figure  ^  ghown  to  be  sjmjlar  fo  pjg   8?> 

except  that  it    has  an  additional    portion 

marked  "Section."    This  section  is  the  true  shape  of  the  oblique  plane 
whereon  the  wreath  ascends,  a  view  of  which  is  given  in  Fig.  88.    It 
will  be  observed  that  one  side  of  it  is  the  developed  tangent  m;  another 
side,  the  developed  tangent    a"    (=   a). 
The    angle    between    the    two   as    here 
presented  is  the  one  required  on  the  face- 
mould  to  square  the  joints. 

In  this  example,  Fig.  89,  owing  to 
the  plane  being  oblique  in  one  direction 
only,  the  shape  of  the  section  is  found  by 
merely  drawing  the  tangent  a"  at  right 
angles  to  the  tangent  ra,  making  it  equal 
in  length  to  the  level  tangent  a  in  the 
plan.     By  drawing  lines  parallel  to   a"       Talent  a 
and  ra  respectively,  the  form  of  the  section   Flg.  gg    Plan  Llne  of  Rail  Pro. 
will  be  found,  its  outlines  being  the  por-         d  VSSKSSS* 
jections  of  the  plan  lines;  and  the  angle 

between  the  two  tangents,  as  already  said,   is  the  angle  required  on 
the  face-mould  to  square  the  joints  of  the  wreath. 

The  solution  here  presented  will  enable  the  student  to  find  the 


STAIR-BUILDING 


47 


correct  direction  of  the  tangents  as  required  on  the  face-mould  to 
square  joints,  in  all  cases  of  practical  work  where  one  tangent  of  a 
wreath  is  level  and  the  other  tangent  is  inclined,  a  condition  usually 
met  with  in  level-landing  stairways. 

Fig.  90  exhibits  a  condition  of  tangents  where  the  two  are  equally 
inclined.  The  plan  here  also  is  taken  from  Fig.  86.  The  inclination 
of  the  tangents  is  made  equal 
to  the  inclination  of  tangent  b 
in  Fig.  86,  as  shown  at  ra  in 
Figs.  87,  88,  and  89. 

In  Fig.  91,  a  view  of  Fig.  90 
is  given,  showing  clearly  the 
inclination  of  the  tangents  c" 
and  d"  over  and  above  the  plan 
tangents  c  and  d.  The  central 
line  of  the  wreath  is  shown 
extending  along  the  sectional 
plane,  over  and  above  its  plan 
lines,  from  one  joint  to  the 
other,  and,  at  the  joints,  made 
square  to  the  inclined  tangents 
c"  and  d".  It  is  evident  from 
the  view  here  given,  that  the 
condition  necessary  to  square  the  joint  at  each  end  would  be  to  find 
the  true  angle  between  the  tangents  c"  and  d",  which  would  give  the 
correct  direction  to  each  tangent. 

In  Fig.  92  is  shown  how  to  find  this  angle  correctly  as  required 
on  the  face-mould  to  square  the  joints.  In  this  figure  is  shown  the 
same  plan  as  in  Figs.  90  and  9J .  and  the  same  inclination  to  the 
tangents  as  in  Fig.  90,  so  that,  except  for  the  portion  marked  "Section," 
it  would  be  similar  to  Fig.  90. 

To  find  the  correct  angle  for  the  tangents  of  the  face-mould, 
draw  the  line  m  from  d,  square  to  the  inclined  line  of  the  tangents 
c'  d";  revolve  the  bottom  inclined  tangent  cf  to  cut  line  m  in  n,  where 
the  joint  is  shown  fixed ;  and  from  this  point  draw  the  line  c"  to  w.  The 
intersection  of  this  line  with  the  upper  tangent  d"  forms  the  correct 
angle  as  required  on  the  face-mould.  By  drawing  the  joints  square 
to  these  two  lines,  they  will  butt  square  with  the  rail  that  is  to  connect 


Joint 
Fig.  89.    Finding  Angle  between  Tangents. 


•18 


STAIR-BUILDING 


Joint 


Fig.  90.    Two  Tangents  Equally 
Inclined. 


Fig.  91.      Plan   Lines   Projected 

into   Oblique  Plane   Inclined   to 

Two  Sides. 


with  them,  or  to  the  joint  of  another  wreath  that  may  belong  to  the 

cylinder  or  well-hole. 

Fig.  93  is  another  view  of 
these  tangents  in  position 
placed  over  and  above  the 
plan  tangents  of  the  well- 
hole.  It  will  be  observed 
that  this  figure  is  made  up 
of  Figs.  88  and  91  com- 
bined. Fig.  88,  as  here 
presented,  is  shown  to  con- 
nect with  a  level  -  landing 
rail  at  a.  The  joint  having 
been  made  square  to  the 
level  tangent,  a  will  butt 
square  to  a  square  end  of 
the  level  rail.  The  joint  at 
h  is  shown  to  connect  the 
two  wreaths  and  is  made 

Fig.  92.    Finding  Angle  between  Tangents.  Square  to  the    inclined    tan- 


\ 


STAIR-BUILDING 


gentra  of  the  lower  wreath,  and  also  square  to  the  inclined  tangent  <? 
of  the  upper  wreath;  the  two  tangents,  aligning,  guarantee  a  square 
butt-joint.  The  upper  joint  is  made  square  to  the  tangent  d",  which 
is  here  shown  to  align  with  the  rail  of  the  connecting  flight;  the  joint 
will  consequently  butt  square  to  the  end  of  the  rail  of  the  flight  above. 
The  view  given  in  this  diagram  is  that  of  a  wreath  starting  from 
a  level  landing,  and  winding  around  a  well-hole,  connecting  the 
landing  with  a  flight  of  stairs  leading  to  a  second  story.  It  is  presented 
to  elucidate  the  use  made  of  tangents  to  square  the  joints  in  wreath 
construction.  The  wreath  is  shown  to 
be  in  two  sections,  one  extending  from 
the  level-landing  rail  at  a  to  a  joint  in 
the  center  of  the  well-hole  at  h,  this 
section  having  one  level  tangent  a  and 
one  inclined  tangent  m;  the  other  sec- 
tion is  shown  to  extend  from  h  to  n, 
where  it  is  butt-jointed  to  the  rail  of  the 
flight  above. 

This  figure  clearly  shows  that  the 
joint  at  a  of  the  bottom  wreath — owing 
to  the  tangent  a  being  level  and  there- 
fore aligning  with  the  level  rail  of  the 
landing — will  be  a  true  butt-joint;  and 
that  the  joint  at  h,  which  connects  the 
two  wreaths,  will  also  be  a  true  butt- 

v  i  ;  joint,  owing  to  it  being  made  square  to 

V'      \  ,u- .       „./._  tne  tangent  m  of 

the  bottom 
wreath  and  to  the 
tangent  c"  of  the 
upper  wreath, 
both  tangents 
having  the  same 
inclination;  also 
the  joint  at  n  will 
butt  square  to 

!g.  93.    Laying  Out  Line  of  Wreath  to  Start  from  Level-Land-    *ne     ra"    °*    "1C 
g  Rail,  Wind  around  Well-Hole,  and  Connect  at  Landing  with    a-    \  ±  i 

Flight  to  Upper  Story.  night       a  D  O  V  6  , 


Fig. 
in 


50 


STAIR-BUILDING 


owing  to  it  being  made  square  to  the  tangent  d",  which  is  shown  to 
have  the  same  inclination  as  the  rail  of  the  flight  adjoining. 

As  previously  stated,  the  use  made  of  tangents  is  to  square  the 
joints  of  the  wreaths;  and  in  this  diagram  it  is  clearly  shown  that  the 
way  they  can  be  made  of  use  is  by  giving  each  tangent  its  true  direc- 
tion. How  to  find  the  true  direction,  or  the  angle  between  the  tangents 


Fig.  94.    Tangents  Unfolded  to  Find  Their  Inclination. 

a  and  m  shown  in  this  diagram,  was  demonstrated  in  Fig.  89;  and  how 
to  find  the  direction  of  the  tangents  c"  and  d"  was  shown  in  Fig.  92. 

Fig.  94  is  presented  to  help  further  toward  an  understanding 
of  the  tangents.  In  this  diagram  they  are  unfolded;  that  is,  they 
are  stretched  out  for  the  purpose  of  finding  the  inclination  of  each 
one  over  and  above  the  plan  tangents.  The  side  plan  tangent  a 
is  shown  stretched  out  to  the  floor  line,  and  its  elevation  a'  is  a  level 
line.  The  side  plan  tangent  d  is  also  stretched  out  to  the  floor  line, 
as  shown  by  the  arc  n'  m'.  By  this  process  the  plan  tangents  are  now 
in  one  straight  line  on  the  floor  line,  as  shown  from  w  to  m' '.  Upon 
each  one,  erect  a  perpendicular  line  as  shown,  and  from  m!  measure 
to  n,  the  height  the  wreath  is  to  ascend  around  the  well-hole.  In 


STAIR-BUILDING 


51 


practice,  the  numlx>r  of  risers  in  the  well-hole  will  determine  this 
height. 

Now,  from  point  n,  draw  a  few  treads  and  risers  as  shown;  and 
along  the  nosing  of  the  steps,  draw  the  pitch-line;  continue  this  line 
over  the  tangents  d",  c",  and  m,  down  to  where  it  connects  with  the 
hot  om  level  tangent,  as  shown.  This  gives  the  pitch  or  inclination 
to  the  tangents 
over  and  above 
the  well-hole. 
The  same  line  is 
shown  in  Fig.  93, 
folded  around 
the  wel  1-hole, 
from  n,  where  it 
connects  with  the 
flight  at  the  up- 
per end  of  the 
well-hole,  to  a, 
where  it  connects 
with  the  level- 
landing  rail  at 
the  bottom  of 
the  well-hole.  It 
will  be  observed 
that  the  upper 
portion,  from 
joint  n  to  joint  h, 
over  the  tangents 

c"  and  d",  coincides  with  the  pitch-line  of  the  same  tangents  as 
presented  in  Fig.  92,  where  they  are  used  to  find  the  true  angle  between 
the  tangents  as  it  is  required  on  the  face-mould  to  square  the  ioints 
of  the  wreath  at  h. 

In  Fig.  89  the  same  pitch  is  shown  given  to  tangent  m  as  in  Fig. 
94;  and  in  both  figures  the  pitch  is  shown  to  be  the  same  as  that  over 
and  above  the  upper  connecting  tangents  c"  and  d",  which  is  a  neces- 
sary condition  where  a  joint,  as  shown  at  h  in  Figs.  93  and  94,  is  to 
connect  two  pieces  of  wreath  as  in  this  example. 

In  Fig.  94  are  shown  the  two  face-moulds  for  the  wreaths,  placed 


Riser 


Fig.  95.    Well-Hole  Connecting  Two  Plights,  with  Two  Wreath- 
Pieces,  Each  Containing  Portions  of  Unequal  Pitch. 


52 


STAHl-BUILDING 


upon  the  pitch-line  of  the  tangents  over  the  well-hole.  The  angles 
between  the  tangents  of  the  face-moulds  have  been  found  in  this 
figure  by  the  same  method  as  in  Figs.  89  and  92,  which,  if  compared 
with  the  present  figure,  will  be  found  to  correspond,  excepting  only 
the  curves  of  the  face-moulds  in  Fig.  94. 

The  foregoing  explanation  of  the  tangents  will  give  the  student 
a  fairly  good  idea  of  the  use  made  of  tangents  in  wreath  construction. 
The  treatment,  however,  would  not  be  complete  if  left  off  at  this 
point,  as  it  shows  how  to  handle  tangents  under  only  two  conditions  — 
namely,  first,  when  one  tangent  inclines  and  the  other  is  level,  as  at 
a  and  m;  second,  when  both  tangents  incline,  as  shown  at  c"  and  d". 

In  Fig.  95  is  shown  a  well-hole  connecting  two  flights,  where  two 


/ 

1    \2 

1, 

Tangent 

Tangent 

1" 

Fig.  90.     Finding  Angle   be- 
tween Tangents  for  Bottom 
Wreath  of  Fig.  95. 


.Joint 

Joint 
h  64  Tangent     I  5 

Fig.  97.     Finding  Angle  be- 
n  Tang 
Wreat 


.      . 

tween   Tangents    for   Upper 
ath  of  Fig.  95. 


portions  of  unequal  pitch  occur  in  both  pieces  of  wreath.  The  first 
piece  over  the  tangents  a  and  b  is  shown  to  extend  from  the  square 
end  of  the  straight  rail  of  the  bottom  flight,  to  the  joint  in  the  center 
of  the  well-hole,  the  bottom  tangent  a"  in  this  wreath  inclining  more 
than  the  upper  tangent  b".  The  other  piece  of  wreath  is  shown  to 
connect  with  the  bottom  one  at  the  joint  h"  in  the  center  of  the  well- 
hole,  and  to  extend  over  tangents  c"  and  d"  to  connect  with  the  rail  of 
the  upper  flight.  The  relative  inclination  of  the  two  tangents  in  this 
wreath,  is  the  reverse  of  that  of  the  two  tangents  of  the  lower  wreath. 
In  the  lower  piece,  the  bottom  tangent  a",  as  previously  stated, 
inclines  considerably  more  than  does  the  upper  tangent  //';  while 
in  the  upper  piece,  the  bottom  tangent  c"  inclines  considerably  less 
than  the  upper  tangent  d". 

The  question  may  arise:  What  caases  this?  Is  it  for  variation 
in  the  inclination  of  the  tangents  over  the  well-hole?  It  is  simply 
owing  to  the  tangents  being  used  in  handrailing  to  square  the  joints. 

The  inclination  of  the  bottom  tangent  a"  of  the  bottom  wreath 


STAIR-BUILDING 


53 


'Joint 


Joint 


is  clearly  shown  in  the  diagram  to  be  determined  by  the  inclination 
of  the  bottom  flight.  The  joint  at  a"  is  made  square  to  both  the  straight 
rail  of  the  flight  and  to  the  bottom  tangent  of  the  wreath;  the  rail  and 
tangent,  therefore,  must  be  equally  inclined,  otherwise  the  joint  will 
not  be  a  true  butt-joint.  The  same  remarks  apply  to  the  joint  at  5, 
where  the  upper  wreath  is  shown  jointed  to  the  straight  rail  of  the 
upper  flight.  In  this  case,  tangent  d"  must  be  fixed  to  incline  conform- 
ably to  the  in- 
clination of  the 
upper  rail;  other- 
wise the  joint  at 
5  will  not  be  a 
true  butt-joint. 

The  same 
principle  is  ap- 
plied in  deter- 
mining the  pitch 
or  inclination 
over  the  crown 
tangents  6"  and 
d'.  Owing  to  the 
necessity  of  joint- 
ing the  two 
wreaths,  as 
shown  at  h,  these 
two  tangents 
must  have  the 

same  inclination,  and   therefore  must  be  fixed,  as  shown   from  2 
to  4,  over  the  crown  of  the  well-hole. 

The  tangents  as  here  presented  are  those  of  the  elevation,  not 
of  the  face-mould.  Tangent  a"  is  the  elevation  of  the  side  plan  tan- 
gent a;  tangents  b"  and  cf  are  shown  to  be  the  elevations  of  the  plan 
tangents  b  and  c;  so,  also,  is  the  tangent  d"  the  elevation  of  the  side 
plan  tangent  d. 

If  this  diagram  were  folded,  as  Fig.  94  was  shown  to  be  in  Fig. 
93,  the  tangents  of  the  elevation — namely,  a",  b",  c",  d" — would  stand 
over  and  above  the  plan  tangents  a,  b,  c,  d  of  the  well-hole.  In  prac- 
tical work,  this  diagram  must  be  drawn  full  size.  It  gives  the  correct 


Fig.  98.    Diagram  of  Tangents  and  Face-Mould  for  Sta'r  with 
Well-Hole  at  Upper  Landing. 


54 


STAIR-BUILDING 


length  to  each  tangent  as  required  on  the  face-mould,  and  furnishes 
also  the  data  for  the  lay-out  of  the  mould. 

Fig.  96  shows  how  to  find  the  angle  between  the  tangents  of  the 
face-mould  for  the  bottom  wreath,  which,  as  shown  in  Fig.  95,  is  to 
span  over  the  first  plan  quadrant  a  6.     The  elevation 
Joi-nt    tangents  a"  and  6",  as  shown,  will  be  the  tangents  of  the 
mould.    To  find  the  angle  between  the  tangents,  draw 
the  line  a  h  in  Fig.  96  ;  and  from  a,  measure  to  2  the 
length   of   the    bottom   tangent   a"    in    Fig.    95;    the 
length  from  2  to  h,  Fig   96,  will  equal  the^  length  of 
the  upper  tangent  6",  Fig.  95. 

From  2  to  1  ,  measure  a  distance  equal  to  2-1  in  Fig. 
95,  the  latter  being  found  by  dropping  a  perpendicular 
from  w  to  meet  the  tangent  b"  extended.  Upon  1,  erect 


Plan!11  d  a  perpendicular  line;  and  placing  the  dividers  on  2, 
extend  to  a;  turn  over  to  the  perpendicular  at  a";  con- 
nect this  point  with  2,  and  the  line  will  be  the  bottom  tangent  as 
required  on  the  face-mould.  The  upper  tangent  will  be  the  line  2-h, 
and  the  angle  between  the  two  lines  is  shown  at  2.  Make  the  joint 
at  h  square  to  2-h,  and  at  a"  square  to  a"-2. 

The  mould  as  it  appears  in  Fig.  96  is  complete,  except  the  curve, 
which  is  comparatively  a 
small  matter  to  put  on,  as 
will  be  shown  further  on. 
The  main  thing  is  to  find 
the  angle  between  the  tan- 
gents, which  is  shown  at  2, 
to  give  them  the  direction  to 
square  the  joints. 

In  Fig.  97  is  shown  how 
to  find  the  angle  between 
the    tangents    c"    and    d" 
shown  in  Fig.  95,  as  required    Fig-  loa  Plan  gSS  ltea^.and  stringer  at 
on  the  face-mould.    On  the 

line  h-5,  make  h-4  equal  to  the  length  of  the  bottom  tangent  of  the 
wreath,  as  shown  at  h"-4  in  Fig.  95;  and  4-5  equal  to  the  length  of 
the  upper  tangent  d".  Measure  from  4  the  distance  shown  at  4-6 
in  Fig  95,  and  place  it  from  4  to  6  as  shown  in  Fig.  97;  upon  6  erect  a 


STAIR-BUILDING 


55 


perpendicular  line.  Now  place  the  dividers  on  4;  extend  to  h;  turn 
over  to  cut  the  perpendicular  in  h";  connect  this  point  with  4,  and  the 
angle  shown  at  4  will  be  the  angle  required  to  square  the  joints  of  the 
wreath  as  shown  at  h"  and  5,  where  the  joint  at  5  is  shown  drawn 
square  to  the  line  4-5,  and  the  joint  at  h"  square  to  the  line  4  h". 

Fig.  98  is  a  diagram  of  tangents  and  face-mould  for  a  stairway 
having  a  well-hole 
at  the  top  landing. 
The  tangents  in  this 
example  will  be  two 
equally  inclined  tan- 
gents for  the  bot- 
tom wreath ;  and  for 
the  top  wreath,  one 
inclined  andonelev- 
el,  the  latter  align- 
ing with  the  level 
rail  of  the  landing. 
The  face-mould, 
as  here  presented, 
will  further  help 
toward  an  under- 
standing of  the  lay- 


Fig.  101. 


Finding  Angle  between  Tangents  for  Squaring 
Joi   -      ' 


Joints  of  Ramped  Wreath. 


out  of  face-moulds 
as  shown  in  Figs.  96 

and  97.  It  will  be  observed  that  the  pitch  of  the  bottom  rail  is  con- 
tinued from  a"  to  b",  a  condition  caused  by  the  necessity  of  jointing  the 
wreath  to  the  end  of  the  straight  rail  at  a",  the  joint  being  made  square 
to  both  the  straight  rail  and  the  bottom  tangent  a".  From  b"  a  line  is 
drawn  to  d",  which  is  a  fixed  point  determined  by  the  number  of  risers 
in  the  well-hole.  From  point  d",  the  level  tangent  d"  5  is  drawn  in  line 
with  the  level  rail  of  the  landing;  thus  the  pitch-line  of  the  tangents 
over  the  well-hole  is  found,  and,  as  was  shown  in  the  explanation  of 
Fig.  95,  the  tangents  as  here  presented  will  be  those  required  on  the 
face-mould  to  square  the  joints  of  the  wreath. 

In  Fig.  98  the  tangents  of  the  face-mould  for  the  bottom  wreath 
are  shown  to  be  a"  and  b".  To  place  tangent  a"  in  position  on  the 
face-mould,  it  is  revolved,  as  shown  by  the  arc,  to  m,  cutting  a  line 


56 


STAIR-BUILDING 


previously  drawn  from  w  square  to  the  tangent  b"  extended.  Then, 
by  connecting  m  to  b",  the  bottom  tangent  is  placed  in  position  on  the 
face-mould.  The  joint  at  m  is  to  be  made  square  to  it;  and  the  joint 
at  c,  the  other  end  of  the  mould,  is  to  be  made  square  to  the  tangent  b". 

The  upper  piece  of  wreath  in  this 
example  is  shown  to  have  tangent  c" 
inclining,  the  inclination  being  the  same 
as  that  of  the  upper  tangent  b"  of  the 
bottom  wreath,  so  that  the  joint  at  c", 
when  made  square  to  both  tangents, 
will  butt  square  when  put  together. 
The  tangent  d"  is  shown  to  be  level,  so 
that  the  joint  at  5,  when  squared  with 
it,  will  butt  square  with  the  square  end 
The  level  tangent  is  shown  revolved  to  its 
In  this  last  position,  it 


Fig .  102.    Bottom  Steps  with  Obtuse- 
Angle  Plan. 


of  the  level-landing  rail, 
position  on  the  face-mould,  as  from  5  to  2. 
will  be  observed  that  its  angle  with  the  inclined  tangent  c"  is  a  right 
angle;  and  it  should  be  remembered  that  in  every  similar  case  where 
one  tangent  inclines  and  one  is  level 
over  a  square-angle  plan  tangent,  the 
angle  between  the  two  tangents  will 
be  a  right  angle  on  the  face-mould. 
A  knowledge  of  this  principle  will  en- 
able the  student  to  draw  the  mould 
for  this  wreath,  as  shown  in  Fig.  99, 
by  merely  drawing  two  lines  perpen- 
dicular to  each  other,  as  d"  5  and  d"  c", 
equal  respectively  to  the  level  tangent 
d"  5  and  the  inclined  tangent  c"  in  Fig. 
98.  The  joint  at  5  is  to  be  made 
square  to  d"  5;  and  that  at  c",  to  d"  c". 
Comparing  this  figure  with  the  face- 
mould  as  shown  for  the  upper  wreath  in  Fig.  98,  it  will  be  observed 
that  both  are  alike. 

In  practical  work  the  stair-builder  is  often  called  upon  to  deal 
with  cases  in  which  the  conditions  of  tangents  differ  from  all  the 
examples  thus  far  given.  An  instance  of  this  sort  is  shown  in  Fig.  100, 
in  which  the  angles  between  the  tangents  on  the  plan  are  acute. 


Fig.  103.    Developing  Face -Mould, 
Obtuse-Angle  Plan. 


STAIR-BUILDING 


r>7 


Fig.  105.    Wreath  Twisted,  Ready  to  be  Moulded. 


In  all  the  preceding  examples,  the  tan- 
gents on  the  plan  were  at  right  angles; 
that  is,  they  were  square  to  one  another. 
Fig.  100  is  a  plan  of  a  few  curved 
steps  placed  at  the  bottom  of  a  stairway 
with  a  curved  stringer, which  is  struck  from 
a  center  o.    The  plan  tangents  a  and  b 
Fig.  104.  cumngwreath  from  are  shown  to  form  an  acute  angle  with  each 
other.    The  rail   above  a  plan  of  this 

design  is  usually  ramped  at  the  bottom  end,  where  it  intersects  the 
newel  post,  and,  when  so  treated,  the  bottom  tangent  a  will  have 
to  be  level. 

In  Fig.  101  is  shown 
how  to  find  the  angle  be- 
tween the  tangents  on  the 
face-mould  that  gives  them 
the  correct  direction  for 
squaring  the  joints  of  the 
wreath  when  it  is  determined  to  have  it  ramped.  This  figure  must 
be  drawn  full  size.  Usually  an  ordinary  drawing-board  will  answer 
the  purpose.  Upon  the  board,  reproduce  the  plan  of  the  tangents  and 
curve  of  the  center  line  of  rail  as  shown  in  Fig.  100.  Measure  the  height 

of  5  risers,  as  shown  in 
Fig.  101,  from  the  floor  line 
to  5 ;  and  draw  the  pitch  of 
the  flight  adjoining  the 
wreath,  from  5  to  the  floor 
line.  From  the  newel, 
draw  the  dotted  line  to  w. 
square  to  the  floor  line; 
from  w,  draw  the  \inewm, 
square  to  the  pitch-line  b". 
Now  take  the  length  of  the 
bottom  level  tangent  on  a 
trammel,  or  on  dividers  if 
large  enough,  and  extend 
it  from  n  to  m,  cutting  the 

Fig.  106.    Twisted  Wreath  Raised  to  Position,  with    linedrawn  previously  from 


58 


STAIR-BUILDING 


w,  at  m.  Connect  m  to  n  as  shown  by  the  line  a".  The  intersection 
of  this  line  with  6"  determines  the  angle  between  the  two  tangents  a" 
and  6"  of  the  face-mould,  which  gives  them  the  correct  direction  as 
required  on  the  face-mould  for  squaring  the  joints.  The  joint  at  m  is 
made  square  to  tangent  a";  and  the  joint  at  5,  to  tangent  b". 

In  Fig.  102  is  presented  an  example  of  a  few  steps  at  the  bottom 
of  a  stairway  in  which  the  tangents  of  the  plan  form  an  obtuse  angle 
with  each  other.  The  curve  of  the 
central  line  of  the  rail  in  this  case 
will  be  less  than  a  quadrant,  and, 
as  shown,  is  struck  from  the  center 
o,  the  curve  covering  the  three  first 
steps  from  the  newel  to  the  springing. 

In  Fig.  103  is  shown  how  to 
develop  the  tangents  of  the  face- 
mould.  Reproduce  the  tangents  and 


Fig.  107.   Finding  Bevsl,  Bot- 
tom Tangent  Inclined,  Top       Fig.  108.    Application  of  Bevels  in   Fitting  Wreath  to 
One  Level.  Kail. 

curve  of  the  plan  in  full  size.  Fix  point  3  at  a  height  equal  to  3 
risers  from  the  floor  line;  at  this  point  place  the  pitch-board  of  the 
flight  to  determine  the  pitch  over  the  curve  as  shown  from  3  through 
b"  to  the  floor  line.  From  the  newel,  draw  a  line  to  iu,  square  to 
the  floor  line;  and  from  w,  square  to  the  pitch-line  b",  draw  the  line 
w  m;  connect  m  to  n.  This  last  line  is  the  development  of  the  bottom 
plan  tangent  a;  and  the  line  b"  is  the  development  of  the  plan  tangent 


STAIR-BUILDING 


6;  and  the  angle  l>etween  the  two  lines  a"  and  b"  will  give  each  line 
its  true  direction  as  required  on  the  face-mould  for  squaring  the  joints 

of  the  wreath, 

a d  xas    shown   at 

ra  to  connect 
square  with 
the  newel,  and 
at  3  to  con- 
nect square  to 
the  rail  of  the 
connecting 
flight. 

The  wreath 
in  this  ex- 
ample follows 

Fig.  109.    Face-Mould  and  Bevel  for  Wreath,  Bottom  Tangent  Level,  +1      r^^oi^^i:.,,, 
Top  One  Inclined.  uie  W««^Ull 

of    the    steps 

without  being  ramped  as  it  was  in  the  examples  shown  in  Figs.  100 
and  101.  In  those  figures  the  bottom  tangent  a  was  level,  while  in 
Fig.  103  it  inclines  equal  to  the  pitch  of  the  upper  tangent  b"  and  of  the 
flight  adjoining.  In 
other  words,  the 
method  shown  in 
Fig.  101  is  applied 
to  a  construction  in 
which  the  wreath  is 
ramped;  while  in  G, 

Fig.  103  the  method 
is  applicable  to  a  (ground 
wreath  following 
the  nosing  line  all 
along  the  curve  to 
the  newel. 

The  stair-build- 
er   is    supposed    to 
know  how  to   con- 
struct a  wreath  under  lx>th  conditions,  as  the  conditions  are  usually 
Jetermined  by  the  Architect. 


Fig.  110.    Finding  Bevels  for  Wreath  with  Two  Equally 
Inclined  Tangents. 


60 


STAIR-BUILDING 


The  foregoing  examples  cover  all  conditions  of  tangents  that 
are  likely  to  turn  up  in  practice,  and,  if  clearly  understood,  will  enable 
the  student  to  lay  out  the 
face-moulds  for  all  kinds 
of  curves. 

Bevels  to  Square  the 
Wreaths.  The  next 
process  in  the  construc- 
tion of  a  wreath  that  the 
handrailer  will  be  called 
upon  to  perform,  is  to  find 
the  bevels  that  will,  by 
being  applied  to  each  end 
of  it,  give  the  correct  angle 
to  square  or  twist  it  when 
winding  around  the  well- 
hole  from  one  flight  to 
another  flight,  or  from 
a  flight  to  a  landing,  as 
the  case  may  be. 

The  wreath  is  first 
cut  from  the  plank  square  to  its  surface  as  shown    in  Fig.   104. 
After    the    application    of   the    bevels,    it    is     twisted,    as  shown 

in  Fig.  105,  ready 
to  be  moulded; 
and  when  in 
position,  ascending 
from  one  end  of  the 
curve  to  the  other 
end,  over  the  in- 
clined plane  of  the 
section  around  the 
well-hole,  its  sides 
will  be  plumb,  as 
shown  in  Fig.  106 
at  b.  In  this  fig- 
ure, as  also  in  Fig.  105,  the  wreath  a  lies  in  a  horizontal  position 
in  which  its  sides  appear  to  be  out  of  plumb  as  much  as  the  bevels 


pig.  in. 

on  Plane 


Application  of  Bevels  to  Wreath  Ascending 
ne  Inclined  Equally  in  Two  Directions. 


Fig.  112.    Finding  Bevel  Where  Upper  Tangent  Inclines 
More  Than  Lower  One. 


STAIR-BUILDING 


61 


Finding  Bevel  Where  Upper  Tangent  Inclines 
Than  Lower  One. 


are  out  of  plumb.     In  the   upper  part   of  the  figure,  the  wreath 

b  is  shown  placed  in  its   position   upon  the  plane  of  the  section, 

where    its    sides    are    seen    to    be    plumb.       It    is    evident,    as 

shown  in  the 

relative    posi- 

tionof  the 

wreath  in  this 

figure,  that,  if 

the  bevel  is  the 

correct    angle 

of  the  plane  of 

the  section 

whereon     the 

wreath  b  rests 

in   its   ascent 

over  the  well- 

hole,      the      Fig.  us. 

wreath  will  in 

that  case  have  its  sides  plumb  all  along  when  in  position.  It  is  for  this 

purpose  that  the  bevels  are  needed. 

A  method  of  finding  the  bevels  for  all  wreaths  (which  is  considered 
i-ather  difficult)  will  now  be  explained : 

First  Case.  In  Fig.  107  is  shown  a  case  where  the  bottom 
tangent  of  a  wreath  is  inclining,  and  the  top  one  level,  similar  to  the 
top  wreath  shown  in  Fig.  98.  It  has  already  been  noted  that  the  plane 
of  the  section  for  this  kind  of  wreath  inclines  to  one  side  only;  therefore 
one  bevel  only  will  be  required  to  square  it,  which  is  shown  at  d, 
Fig.  107.  A  view  of  this  plane  is  given  in  Fig.  108;  and  the  bevel  d, 
as  there  shown,  indicates  the  angle  of  the  inclination,  which  also  is 
the  bevel  required  to  square  the  end  d  of  the  wreath.  The  bevel  is 
shown  applied  to  the  end  of  the  landing  rail  in  exactly  the  same  manner 
in  which  it  is  to  be  applied  to  the  end  of  the  wreath.  The  true  bevel 
for  this  wreath  is  found  at  the  upper  angle  of  the  pitch-board.  At  the 
end  a,  as  already  stated,  no  bevel  is  required,  owing  to  the  plane 
inclining  in  one  direction  only.  Fig.  109  shows  a  face-mould  and 
bevel  for  a  wreath  with  the  bottom  tangent  level  and  the  top  tangent 
inclining,  such  as  the  piece  at  the  bottom  connecting  with  the  landing 
rail  in  Fig.  94. 


r>2 


STAIR-BUILDING 


Second  Case.  It  may  be  required  to  find  the  bevels  for  a  wreath 
having  two  equally  inclined  tangents.  An  example  of  this  kind  also 
is  shown  in  Fig.  94,  where  both  the  tangents  c"  and  d"  of  the  upper 


Fig.  114.  Finding  Bevel 
Where  Tangents  In- 
cline Equally  over 
Obtuse-Angle  Plan. 


Fig.  115.    Same  Plan  as  in  Fig. 

114,  but  with  Bottom  Tangent 

Level. 


wreath  incline  equally.  Two  bevels  are  required  in  this  case,  because 
the  plane  of  the  section  is  inclined  in  two  directions;  but,  owing  to  the 
inclinations  being  alike,  it  follows  that  the  two  will  be  the  same. 
They  are.to  be  applied  to  both  ends  of  the  wreath,  and,  as  shown  in 
Fig.  105,  in  the  same  direction— namely, 
toward  the  inside  of  the  wreath  for  the  bot- 
tom end,  and  toward  the  outside  for  the  upper 
end. 

In  Fig.  110  the  method  of  finding  the  bevels 
is  shown.  A  line  is  drawn  from  w  to  c",  square 
to  the  pitch  of  the  tangents,  and  turned  over 
to  the  ground  line  at  h,  which  point  is  con- 
nected to  a  as  shown.  The  bevel  is  at  h. 
To  show  that  equal  tangents  have  equal 
bevels,  the  line  m  is  drawn,  having  the  same 

inclination  as  the  bottom  tangent  c",  but  in  another  direction.  Place 
the  dividers  on  o',  and  turn  to  touch  the  lines  d"  and  TO,  as  shown  by 
the  semicircle.  The  line  from  o'  to  n  is  equal  to  the  side  plan  tangent 


Fig.  116.    Finding  Bevels 
for  Wreath  of  Fig.  115. 


STAIR-BUILDING 


w  a,  and  both  the  bevels  here  shown  are  equal  to  the  one  already 
found.  They  represent  the  angle  of  inclination  of  the  plane  where- 
on the  wreath  ascends,  a  view  of  which  is  given  in  Fig.  Ill,  where 
the  plane  is  shown  to  incline  equally  in  two  directions.  At  both  ends 
is  shown  a  section  of  a  rail ;  and  the  bevels  are  applied  to  show  how, 
by  means  of  them,  the  wreath  is  squared  or  twisted  when  winding 
around  the  well-hole  and  ascending  upon  the  plane  of  the  section. 
The  view  given  in 

this  figure  will  en-  >Xf 

able  the  student  to     f\  m 

understand  the 
nature  of  the  bevels 
found  in  Fig.  110 
for  a  wreath  having 
two  equally  inclined 
tangents;  also  for 
all  other  wreaths  of 
equally  inclined 
tangents,  in  that 
every  wreath  in 
such  case  is  assumed 
to  rest  upon  an  in- 
clined plane  in  its 
ascent  over  the  well- 
hole,  the  bevel  in 
every  case  being  the  angle  of  the  inclined  plane. 

Third  Case.  In  this  example,  two  unequal  tangents  are  given, 
the  upper  tangent  inclining  more  than  the  bottom  one.  The  method 
shown  in  Fig.  110  to  find  the  bevels  for  a  wreath  with  two  equal  tan- 
gents, is  applicable  to  all  conditions  of  variation  in  the  inclination  of 
the  tangents.  In  Fig.  112  is  shown  a  case  where  the  upper  tangent 
d"  inclines  more  than  the  bottom  one  c".  The  method  in  all  cases  is 
to  continue  the  line  of  the  upper  tangent  d",  Fig.  112,  to  the  ground 
line  as  shown  at  n;  from  n,  draw  a  line  to  a,  which  will  be  the  horizon- 
tal trace  of  the  plane.  Now,  from  o,  draw  a  line  parallel  to  a  n,  as 
shown  from  o  to  d,  upon  d,  erect  a  perpendicular  line  to  cut  the  tangent 
d",  as  shown,  at  m;  and  draw  the  line  m  u  o".  Make  u  o"  equal  to 
the  length  of  the  plan  tangent  as  shown  by  the  arc  from  o.  Put  one 


Fig.  117.    Upper  Tangent  Inclined,  Lower  Tangent  Level, 
Over  Acute- Angle  Plan. 


64  STAIR-BUILDING 

leg  of  the  dividers  on  u;  extend  to  touch  the  upper  *angent  d",  and 
turn  over  to  1 ;  connect  1  to  o";  the  bevel  at  1  is  to  be  applied  to  tangent 
d".  Again  place  the  dividers  on  u;  extend  to  the  line  h,  and  turn  over  to 
2  as  shown;  connect  2  to  o",  and  the  bevel  shown  at  2  will  be  the  one 

to  apply  to  the  bottom  tangent  c". 
It  will  be  observed  that  the  line  h 
represents  the  bottom  tangent.  It 
is  the  same  length  and  has  the  same 
inclination.  An  example  of  this 
kind  of  wreath  was  shown  in  Fig. 
95,  where  the  upper  tangent  d"  is 
shown  to  incline  more  than  the  bot- 
a  c  torn  tangent  c"  in  the  top  piece  ex- 

Fig.  118.    Finding  Bevels^or  Wreath        tendingfrom^  to  5.      fievd  1,  found 

in  Fig.  112,  is  the  real  bevel  for  the 

end  5 ;  and  bevel  2,  for  the  end  h"  of  the  wreath  shown  from  h"  to  5 
in  Fig.  95. 

Fourth  Case.  In  Fig.  113  is  shown  how  to  find  the  bevels  for  a 
wreath  when  the  upper  tangent  inclines  less  than  the  bottom  tangent. 
This  example  is  the  reverse  of  the  preceding  one;  it  is  the  condition 
of  tangents  found  in  the  bottom  piece  of  wreath  shown  in  Fig.  95. 
To  find  the  bevel,  continue  the  upper  tangent  b"  to  the  ground  line, 
as  shown  at  n;  connect  n  to  a,  which  will  be  the  horizontal  trace  of 
the  plane.  From  o,  draw  a  line  parallel  to  n  a,  as  shown  from  o  to  d; 
upon  d,  erect  a  perpendicular  line  to  cut  the  continued  portion  of  the 
upper  tangent  b"  in  m;  from  m,  draw  the  line  m  u  o"  across  as  shown. 
Now  place  the  dividers  on  u;  extend  to  touch  the  upper  tangent,  and 
turn  over  to  1 ,  connect  1  to  o";  the  bevel  at  1  will  be  the  one  to  apply 
to  the  tangent  b"  at  h,  where  the  two  wreaths  are  shown  connected  in 
Fig.  95.  Again  place  the  dividers  on  u;  extend  to  touch  the  line  c; 
turn  over  to  2;  connect  2  to  o";  the  bevel  at  2  is  to  be  applied  to  the 
bottom  tangent  a"  at  the  joint  where  it  is  shown  to  connect  with  the 
rail  of  the  flight. 

Fifth  Case.  In  this  case  we  have  two  equally  inclined  tangents 
over  an  obtuse-angle  plan.  In  Fig.  102  is  shown  a  plan  of  this  kind ; 
and  in  Fig.  103,  the  development  of  the  face-mould. 

In  Fig.  114  is  shown  how  to  find  the  bevel.  From  a,  draw  a  line 
to  a',  square  to  the  ground  line.  Place  the  dividers  on  a';  extend  to 


STAIR-BUILDING 


65 


touch  the  pitch  of  tangents,  and  turn  over  as  shown  to  m;  connect  ra 
to  a.  The  bevel  at  m  will  be  the  only  one  required  for  this  wreath, 
but  it  will  have  to  be  applied  to  both  ends,  owing  to  the  two  tangents 
being  inclined. 

Sixth  Case.  In  this  case  we  have  one  tangent  inclining  and  one 
tangent  level,  over  an  acute-angle  plan. 

In  Fig.  115  is  shown  the  same  plan  as  in  Fig.  114;  but  in  this 


Directing  Ordin^te 
Of  Section  \^   \ 


Directing  Odinate 
Of  Base 


Fig.  119.    Laying  Out  Curves  on  Face- Mould  with  Pins  and  String. 

case  the  bottom  tangent  a"  is  to  be  a  level  tangent.  Probably  this 
condition  is  the  most  commonly  met  with  in  wreath  construction  at 
the  present  time.  A  small  curve  is  considered  to  add  to  the  appear- 
ance of  the  stair  and  rail;  and  consequently  it  has  become  almost  a 
"fad"  to  have  a  little  curve  or  stretch-out  at  the  bottom  of  the  stairway, 
and  in  most  cases  the  rail  is  ramped  to  intersect  the  newel  at  right 
angles  instead  of  at  the  pitch  of  the  flight.  In  such  a  case,  the  bottom 
tangent  a"  will  have  to  be  a  level  tangent,  as  shown  at  a"  in  Fig.  115, 
the  pitch  of  the  flight  being  over  the  plan  tangent  b  only. 


STAIR-BUILDING 


Fig.  130.   Simple  Method  of  Drawing  Curves 
on  Pace-Mould. 


To  find  the  bevels  when  tangent  b"  inclines  and  tangent  a"  is 
level,  make  a  c  in  Fig.  116  equal  to  a  c  in  Fig.  115.    This  line  will  be 

the  base  of  the  two  bevels. 
Upon  a,  erect  the  line  a  w  m 
at  right  angles  to  a  c;  make  a 
w  equal  too  win  Fig.  115;  con- 
nect w  and  c;  the  bevel  at  w 
will  be  the  one  to  apply  to  tan- 
gent b"  at  n  where  the  wreath 
is  joined  to  the  rail  of  the  flight. 
Again,  make  a  w  in  Fig.  116 
equal  the  distance  shown  in  Fig. 
115  between  w  and  m,  which  is 
the  full  height  over  which  tan- 
gent b"  is  inclined ;  connect  m  to 
c  in  Fig.  116,  and  at  m  is  the  bevel  to  be  applied  to  the  level  tangent  a". 

Seventh  Case. 
In  this  case,  illus- 
trated in  Fig.  117, 
the  upper  tangent 
b"  is  shown  to  in- 
cline, and  the  bot- 
tom tangent  a"  to 
be  level,  over  an 
acute  -  angle  plan. 
The  plan  here  is 
the  same  as  that  in 
Fig.  100,  where  a 
curve  is  shown  to 
stretch  out  from  the 
line  of  the  straight 
stringer  at  the  bot- 
tom of  a  flight  to  a 
newel,  and  is  large 
enough  to  contain 
five  treads,  which 
are  gracefully  rounded  to  cut  the  curve  of  the  central  line  of  rail  in 
1,  2,  3,  4.  This  curve  also  may  be  used  to  connect  a  landing  rail  to  a 


Fig.  121.    Tangents,  Bevels,  Mould-Curves,  etc.,  from  Bottom 
Wreath  of  Fig.   95,  in  which  Upper  Tangent  Inclines  Lesi 
than  Lower  One. 


STAIR-BUILDING 


67 


_Major 


flight,  either  at  top  or  bottom,  when  the  plan  is  acute-angled,  as  will 
be  shown  further  on. 

To  find  the  bevels— 
for  there  will  be  two 
bevels  necessary  for  this 
wreath,  owing  to  one  /'  ol 

tangent  b"  being  inclined  /  f  | 

and  the  other  tangent  a" 
being  level — make  a  c, 
Fig.  118,  equal  to  a  c  in 
Fig.  117,  which  is  a  line 
drawn  square  to  the 
ground  line  from  the 
newel  and  shown  in  all 
preceding  figures  to  have 
been  used  for  the  base 
of  a  triangle  containing 
the  bevel.  Make  aw  in 
Fig.  118  equal  to  w  o  in 

Fig.  117,  which  is  a  line  drawn  square  to  the  inclined  tangent  b"  from 
w;  connect  w  and  c  in  Fig.  118.  The  bevel  shown  at  w  will  be  the  one 
to  be  applied  to  the  joint  5  on  tangent  b",  Fig.  117.  Again,  make  am 


Fig.    122. 


Developed  Section  of  Plane  Inclining  Un- 
equally in  Two  Directions. 


Fig   123.    Arranging  Risers    around  Well-Hole  on  Level  Landing  Stair, 
with  Radius  of  Central  Line  of  Rail  One-Half  Width  of  Tread. 

in  Fig.  118  equal  to  the  distance  shown  in  Fig.  117  between  the  line 
representing  the  level  tangent  and  the  line  m'  5,  which  is  the  height  that 


STAIR-BUILDING 


tangent  6"  is  shown  to  rise;  connect  m  to  c  in  Fig.  1 18;  the  bevel  shown 
at  m  is  to  be  applied  to  the  end  that  intersects  with  the  newel  as  shown 
at  m  in  Fig.  117. 

The  wreath  is  shown  developed  in  Fig.  101  for  this  case;  so  that, 
with  Fig.  100  for  plan,  Fig.  101  for  the  development  of  the  wreath, 
and  Figs.  117  and  118  for  finding  the  bevels,  the  method  of  handling 
any  similar  case  in  practical  work  «^an  be  found. 

How  to  Put  the  Curves  on  the  Face- Mould.    It  has  been  shown 

how  to  find  the 
angle  between  the 
tangents  o  f  the 
face-mould,  and 
that  the  angle  is 
for  the  purpose  of 
squaring  the  joints 
at  the  ends  of  the 
wreath.  In  Fig. 
119  is  shown  how 
to  lay  out  the 
curves  by  means 
of  pins  and  a 
string — a  very 
common  practice 
among  stair-build- 
ers.  In  this 
example  the  face- 
mould  has  equal 
tangents  as  shown 
at  cf  and  d".  The  angle  between  the  two  tangents  is  shown  at  m  as  it 
will  be  required  on  the  face-mould.  In  this  figure  a  line  is  drawn 
from  m  parallel  tothe  line  drawn  from  A,which  is  marked  in  the  diagram 
as  "Directing  Ordinate  of  Section."  The  line  drawn  from  m  will 
contain  the  minor  axes;  and  a  line  drawn  through  the  corner  of  the 
section  at  3  will  contain  the  major  axes  of  the  ellipses  that  will  consti- 
tute the  curves  of  the  mould. 

The  major  is  to  be  drawn  square  to  the  minor,  as  shown.  Place, 
from  point  3,  the  circle  shown  on  the  minor,  at  the  same  distance  as 
the  circle  in  the  plan  is  fixed  from  the  point  o.  The  diameter 


Fig.  124.    Arrangement  of  Risers  Around  Well-Hole  with  Rad- 
ius Larger  Than  One-Half  Width  of  Tread. 


STAIR-BUILDING 


of  this  circle  indicates  the  width  of  the  curve  at  this  point.    The  width 
at  each  end  is  determined  by  the  bevels.    The  distance  a  6,  as  shown 


Fig.  125.    Arrangement  of  Risers  around  Well-Hole,  with  Risers  Spaced 
Full  Width  of  Tread. 

upon  the  long  edge  of  the  bevel,  is  equal  to  ^  the  width  of  the  mould,  and 
is  the  hypotenuse  of  a  right-angled  triangle  whose  base  is  £  the  width  of 
the  rail.  By  placing  this  dimension  on  each  side  of  n,  as  shown  at  6 


Fig.  ;26.    Plan  of  Stall 
Shown  in  Fig.  123. 


Fig.    127.     Plan    of    Stair 
Shown  In  Fig.  124. 


Fig.  128.     Plan  of  Stair 
Shown  in  Fig.  125. 


and  b,  and  on  each  side  of  h"  on  the  other  end  of  the  mould,  as  shown 
also  at  6  and  b,  we  obtain  the  points  6  2  6  on  the  inside  of  the  curve,  and 


70 


STAIR-BUILDING 


the  points  b  1  b  on  the  outside.  It  will  now  be  necessary  to  find  the 
elliptical  curves  that  will  contain  these  points ;  and  before  this  can  be 
done,  the  exact  length  of  the  minor  and 
major  axes  respectively  must  be  deter- 
mined. The  length  of  the  minor  axis 
for  the  inside  curve  will  be  the  dis- 
tance shown  from  3  to  2;  and  its  length 
for  the  outside  will  be  the  distance 
shown  from  3  to  1 . 

I  Pitch  T°  ^nd  tne  lengtn  of  the  major  axis 

'Board  for  the  inside,  take  the  length  of  half  the 
minor  for  the  inside  on  the  dividers: 
place  one  leg  on  b,  extend  to  cut  the 
major  in  z,  continue  to  the  minor  as 
shown  at  k.  The  distance  from  6  to  k 
will  be  the  length  of  the  semi-major  axis  for  the  inside  curve. 

To  draw  the  curve,  the  points  or  foci  where  the  pins  are  to  be 
fixed  must  be  found  on  the  major  axis.  To  find  these  points,  take 
the  length  of  b  k  (which  is,  as  previously  found,  the  exact  length  of 


Fig.  129.     Drawing  Face-Mould 
for  Wreath  from  Pitch-Board. 


Landing  Rail 


Fig.  130.    Development  of  Face-Mould  for  Wreath  Connecting  Rail 
of  Flight  with  Level-Landing  Rail. 


the  semi-major  for  the  inside  curve)  on  the  dividers;  fix  one  leg  at  2, 
and  describe  the  arc  Y,  cutting  the  major  where  the  pins  are  shown 
fixed,  at  o  and  o.  Now  take  a  piece  of  string  long  enough  to  form  a 


STAIR-BUILDING  71 

loop  around  the  two  and  extending,  when  tight,  to  2,  where  the  pencil 
is  placet! ;  and,  keeping  the  string  tight,  sweep  the  curve  from  b  to  b. 


Step 


Step 


Step 


Step 


Joint 


Fig.  131.    Arranging  Risers  In 

Quarter-Turn  between 

Two  Flights. 


Ratform 


^ 


Joint 


Step 


Step 


The  same  method,  for  finding  the  major  and  foci  for  the  outside 
curve,  is  shown  in  the  diagram.  The  line  drawn  from  b  on  the  outside 
of  the  joint  at  n,  to  w,  is  the  semi-major  for  the  outside  curve;  and  the 


-"Riser 


Fig.  132.    Arrangement  of  Risers  around  Quarter-Turn  Giv- 
ing Taugenu  Equal  Pitch  with  Connecting  Flight. 

points  where  the  outside  pins  are  shown  on  the  major  will  be  the  foci. 
To  draw  the  curves  of  the  mould  according  to  this  method,  which 


72 


STAIR-BUILDING 


is  a  scientific  one,  may  seem  a  complicated  problem;  but  once  it  is 
understood,  it  becomes  very  simple.    A  simpler  way  to  draw  them, 
however,  is  shown  in  Fig.  320. 

The  width  on  the  minor  and  at  each  end 
will  have  to  be  determined  by  the  method  just 
explained  in  connection  with  Fig.  119.  In 
Fig  120,  the  points  b  at  the  ends,  and  the  points 
in  which  the  circumference  of  the  circle  cuts 
the  minor  axis,  will  be  points  contained  in 

the  curves,  as  already  explained.  Now  take  a  flexible  lath;  bend  it 
to  touch  b,  2,  and  b  for  the  inside  curve,  and  b,  w,  and  b  for  the  outside 
curve.  This  method  is  handy  where  the  curve  is  comparatively  flat, 
as  in  the  example  here  shown;  but  where  the  mould  has  a  sharp  curva- 


Fig.  133.    Finding  Bevel 

for  Wreath  of  Plan, 

Fig.  132. 


Fig.  134.    Well-Hole  with  Riser  In  Center.    Tangents  of  Face-Mould,  and  Central  Line 
of  Rail,  Developed. 

ture,  as  in  case  of  the  one  shown  in  Fig.  101,  the  method  shown  in  Fig. 
119  must  be  adhered  to. 

With  a  clear  knowledge  of  the  above  two  methods,  the  student 
will  be  able  to  put  curves  on  any  mould. 

The  mould  shown  in  these  two  diagrams,  Figs.  119  and  120,  is 
for  the  upper  wreath,  extending  from  h  to  n  in  Fig.  94  A  practical 
handrailer  would  draw  only  what  is  shown  in  Fig.  120.  He  would 


STAIR-BUILDING 


7.3 


take  the  lengths  of  tangents  from  Fig.  94,  and  place  them  as  shown 
at  h  m  and  m  n.  By  comparing  Fig.  120  with  the  tangents  of  the 
upper  wreath  in  Fig.  94,  it  will  be  easy  for  the  student  to  understand 


Fig.  135.    Arrangement  of  Risers  in 
Stair  with  Obtuse- Angle  Plan. 


Fig.  136.  Arrangement  of  Risers  in  Obtuse- 
Angle  Plan,  Giving  Equal  Pitch  over  Tan- 
gents and  Flights.  Face-Mould  Developed. 


the  remaining  lines  shown  in  Fig.  120.    The  bevels  are  shown  applied 

to  the  mould  in  Fig.  105,  to  give  it  the  twist.    In  Fig.  106,  is  shown  how, 

after  the  rail  is  twisted  and 

placed  in  position  over  and 

above  the  quadrant  c  d  in 

Fig.  94,  its  sides  will  be 

plumb. 

In  Fig.  121  are  shown 
the  tangents  taken  from 
the  bottom  wreath  in  Fig. 
95  It  was  shown  how  to 
develop  the  section  and 
find  the  angle  for  the  tan- 
gents in  the  face-mould,  Fig-  137.  Arrangement  of  Risers  in  Flight  with 

Curve  at  Lauding. 

in  Fig.  113.    The  method 

shown  in  Fig.  119  for  putting  on  the  curves,  would  be  the  most  suitable. 

Fig.  121  is  presented  more  for  the  purposes  of  study  than  as  a 

method  of  construction.    It  contains  all  the  lines  made  use  of  to  find 


74 


STAIR-BUILDING 


Landing  Rail 


Fig.  188.    Development  of  Face-Moulds 
for  Plan,  Fig.  137. 


the  developed  section  of  a  plane  inclining  unequally  in  two  different 
directions,  as  shown  in  Fig.  122. 

Arrangement  of  Risers  in  and  around  Well-Hole.  An  important 
matter  in  wreath  construction  is  to  have  a  knowledge  of  how  to 

arrange  the  risers  in  and  around  a 
well-hole.  A  great  deal  of  labor 
and  material  is  saved  through  it; 
also  a  far  better  appearance  to  the 
finished  rail  may  be  secured. 

In  ievel-landing  stairways,  the 
easiest  example  is  the  one  shown 
in  Fig.  123,  in  which  the  radius  of 
the  central  line  of  rail  is  made 
equal  to  one-half  the  width  of  a  tread.  In  the  diagram  the  radius  is 
shown  to  be  5  inches,  and  the  treads  10  inches.  The  risers  are  placed 
in  the  springing,  as  at  a  and  a.  The  elevation  of  the  tangents  by  this 
arrangement  will  be,  as  shown,  one  level  and  one  inclined,  for  each 
piece  of  wreath.  When  in  this  position,  there  is  no  trouble  in  finding 
the  angle  of  the  tangent  as  required  on  the  face-mould,  owing  to  that 
angle,  as  in  every  such  case,  being  a  right  angle,  as  shown  at  w;  also 
no  special  bevel  will  have  to  be  found,  because  the  upper  bevel  of  the 
pitch-board  contains  the  angle  required. 

The  same  results  are  obtained  in  the  example  shown  in  Fig. 
124,  in  which  the  radius  of  the  well-hole  is  larger  than  half  the  width 
of  a  tread,  by  placing  the  riser  a  at  a  distance  from  c  equal  to  half 
the  width  of  a  tread,  instead  of  at  the  springing  as  in  the  preceding 
example. 

In  Fig.  125  is  shown  a  case  where  the  risers  are  placed  at  a  dis- 
tance from  c  equal  to  a  full  tread,  the  effect  in  respect  to  the  tangents 
of  the  face-mould  and  bevel  being  the  same  as  in  the  two  preceding 
examples.  In  Fig.  126  is  shown  the  plan  of  Fig.  123;  in  Fig.  127, 
the  plan  of  Fig.  124;  and  in  Fig.  128,  the  plan  of  Fig.  125.  For  the 
wreaths  shown  in  all  these  figures,  there  will  be  no  necessity  of  spring- 
ing the  plank,  which  is  a  term  used  in  hand  railing  to  denote  the 
twisting  of  the  wreath ;  and  no  other  bevel  than  the  one  at  the  upper 
end  of  the  pitch-board  will  be  required.  This  type  of  wreath,  also, 
is  the  one  that  is  required  at  the  top  of  a  landing  when  the  rail  of  the 
flight  intersects  with  a  level-landing  rail. 


STAIR-BUILDING  75 

In  Fig.  129  is  shown  a  very  simple  method  of  drawing  the  face- 
mould  for  this  wreath  from  the  pitch-board.  Make  a  c  equal  to  the 
radius  of  the  plan  central  line  of  rail  as  shown  at  the  curve  in  Fig.  130. 
From  where  line  c  c"  cuts  the  long  side  of  the  pitch-board,  the 
line  c"  a"  is  drawn  at  right  angles  to  the  long  edge,  and  is  made 
equal  to  the  length  of  the  plan  tangent  a  c,  Fig.  130.  The  curve  is 
drawn  by  means  of  pins  and  string  or  a  trammel. 

In  Fig.  131  is  shown  a  quarter-turn  between  two  flights.  The 
correct  method  of  placing  the  risers  in  and  around  the  curve,  is  to  put 
the  last  one  in  the  first  flight  and  the  first  one  in  the  second  flight 
one-half  a  step  from  the  intersection  of  the  crown  tangents.  By 
this  arrangement,  as  shown  in  Fig.  132,  the  pitch-line  of  the 
tangents  will  equal  the  pitch  of  the  connecting  flight,  thus  securing 
the  second  easiest  condition  of  tangents  for  the  face-mould — 
namely,  as  shown,  two  equal  tangents.  For  this  wreath,  only  one 
bevel  will  be  needed,  and  it  is  made  up  of  the  radius  of  the  plan 
central  line  of  the  rail  oc,  Fig.  131,  for  base,  and  the  line  1-2, 
Fig.  132,  for  altitude,  as  shown  in  Fig.  133. 

The  bevel  shown  in  this  figure  has  been  previously  explained  in 
Figs.  105  and  106.  It  is  to  be  applied  to  both  ends  of  the  wreath. 

The  example  shown  in  Fig.  134  is  of  a  well-hole  having  a  riser 
in  the  center.  If  the  radius  of  the  plan  central  line  of  rail  is  made 
equal  to  one-half  a  tread,  the  pitch  of  tangents  will  be  the  same  as 
of  the  flights  adjoining,  thus  securing  two  equal  tangents  for  the  two 
sections  of  wreath.  In  this  figure  the  tangents  of  the  face-mould  are 
developed,  and  also  the  central  line  of  the  rail,  as  shown  over  and 
above  each  quadrant  and  upon  the  pitch-line  of  tangents. 

The  same  method  may  be  employed  in  stairways  having  obtuse- 
angle  and  acute-angle  plans,  as  shown  in  Fig.  135,  in  which  two  flights 
are  placed  at  an  obtuse  angle  to  each  other.  If  the  risers  shown  at 
a  and  a  are  placed  one-half  a  tread  from  c,  this  will  produce  in  the 
elevation  a  pitch-line  over  the  tangents  equal  to  that  over  the  flights 
adjoining,  as  shown  in  Fig.  136,  in  which  also  is  shown  the  face-mould 
for  the  wreath  that  will  span  over  the  curve  from  one  flight  to  another. 

In  Fig.  137  is  shown  a  flight  having  the  same  curve  at  a  landing. 
The  same  arrangement  is  adhered  to  respecting  the  placing  of  the 
risers,  as  shown  at  a  and  a.  In  Fig.  138  is  shown  how  to  develop  the 
face-moulds- 


1 

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PART   II 

THE  STEEL  SQUARE 


Introductory.  The  Standard  Steel  Square  has  a  blade  24 
inches  long  and  2  inches  wide,  and  a  tongue  from  14  to  18  inches  long 
and  1^  inches  wide.  The  blade  is  at  right  angles  to  the  tongue. 

The  face  of  the  square  is  shown  in  Fig.  1.  It  is  always  stamped 
with  the  manufacturer's  name  and  number. 

The  reverse  is  the  back  (see  Fig.  2). 

The  longer  arm  is  the  blade;  the  shorter  arm,  the  tongue. 

In  the  center  of  the  tongue,  on  the  face  side,  will  be  found  two 
parallel  lines  divided  into  spaces  (see  Fig.  1);  this  is  the  octagon  scale. 

The  spaces  will  be  found  numbered  10,  20,  30,  40,  50,  60,  and  70> 
when  the  tongue  is  18  inches  long. 

To  draw  an  octagon  of  8  inches  square,  draw  an  8  inch  square 
and  then  draw  a  perpendicular  and  a  horizontal  line  through  its  cen- 
ter. To  find  the  length  of  the  octagon  side,  place  one  point  of  a  com- 
pass on  any  of  the  main  divisions  of  the  scale,  and  the  other  point  of 
the  compass  on  the  eighth  subdivision;  then  step  this  length  off  on 
each  side  of  the  center  lines  on  the  side  of  the  square,  which  will  give 
the  points  from  which  to  draw  the  octagon  lines. 

The  diameter  of  the  octagon  must  equal  in  inches  the  number  of 
spaces  taken  from  the  square. 

On  the  opposite  side  of  the  tongue,  in  the  center,  will  be  found 
the  brace  rule  (see  Fig.  3).  The  fractions  denote  the  rise  and  run  of 
the  brace,  and  the  decimals  the  length.  For  example,  a  brace  of  36 
inches  run  and  36  inches  rise,  has  a  length  of  50.91  inches;  a  brace 
of  42  inches  run  and  42  inches  rise,  has  a  length  of  59.40  inches;  etc. 

On  the  back  of  the  blade  (Fig.  4)  will  be  found  the  board  measure> 
where  eight  parallel  lines  running  along  the  length  of  the  blade  are 
shown  and  divided  at  every  inch  by  cross-lines.  Under  12,  on  the 
outer  edge  of  the  blade,  will  be  found  the  various  lengths  of  the  boards, 
as  8,  9,  10,  11,  12,  etc.  For  example,  take  a  board  14  feet  long  and  9 


THE  STEEL  SQUARE 


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1  Square,  Showing  Rafter  Table. 

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THE  STEEL  SQUARE 


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THE  STEEL  SQUARE 


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Fig.  5.    Use  of  Steel  Square  to  Find  Miter  and  Side  of 
Pentagon. 


inches  wide.  To 
find  the  contents, 
look  under  12,  and 
find  14;  then  fol- 
low this  space  along 
to  the  cross-line  un- 
der 9,  the  width  of 
the  board  ;  and  here 
is  found  10  feet  6 
inches,  denoting 
the  contents  of  a 
board  14  feet  long 
and  9  inches  wide. 
To  Find  the  Mi= 
ter  and  Length  of 
Side  for  any  Poly= 
gon,  with  the  Steel 
Square.  In  Fig.  5 

is  shown  a  pentagon  figure.    The  miters  of  the  pentagon  stand  at 

72  degrees  with  each  other,  and  are  found  by  dividing  360  by  5,  the 

number  of  sides  in  the  pentagon.    But  the  angle  when  applied  to  the 

square  to  obtain  the  miter,  is  only  one-half  of  72,  or  36 

degrees,  and  intersects  the  blade  at  8f  f  ,  as  shown  in  Fig.  5. 
By  squaring  up  from  6  on  .the  tongue,  intersecting 

the  degree  line  at  a,  the 

center  a   is   determined 

either  for  the  inscribed 

or  the  circumscribed  di- 

ameter, the  radii   being 

a  b    and     a  c,    respec- 

tively. 

The  length  of  the 

sides  will  be  8|f  inches 

to  the  foot. 

If  the  length  of  the 

inscribed  diameter  be  8 

feet,  then  the  sides  would 


!l   I   I   I   I 


,'\  I   I   I   I  I  I   I  I   I  I 


rn 


inches. 


Flg'6'    Use  of  Steel  Squar^Flnd  Miter  and  Side  of 


THE  STEEL  SQUARE 


The  figures  to  use  for  other  polygons  are  as  follows: 
Triangle         20£|- 
Square  12 

Hexagon          7 
Nonagon          4f 
Decagon  3£ 

In  Fig.  6  the  same  process  is  used  in  finding  the 
miter  and  side  of  the  hexagon  polygon. 

To  find  the  degree  line,  360  is  divided  by  6,  the  num- 
ber of  sides,  as  follows: 
360  -T-  6  =  60;  and 
60  -^  2  =  30  degrees. 

Now,  from  12  on 
tongue,  draw  a  line 
making  an  angle  of  30 
degrees  with  the  tongue. 
It  will  cut  the  blade  in 
7  as  shown;  and  from  7 
to  m,  the  heel  of  the 
square,  will  be  the  length 
of  the  side.  From  6  on 
tongue,  erect  a  line  to 
cut  the  degree  line  in  c;  and  with  c  as  center,  describe  a  circle  having 
the  radius  of  c  7;  and  around  the  circle,  complete  the  hexagon  by 
taking  the  length  7  m  with  the  compass  for  each  side,  as  shown. 

In  Fig.  7  the  same  process  is  shown  applied  to  the  octagon.  The 
degree  line  in  all  the  polygons  is  found  by  dividing  360  by  the  number 
of  sides  in  the  figure: 

360  -^  8  =  45;  and  45  -5-  2  =  22  J  degrees. 

This  gives  the  degree  line  for  the  octagon.    Complete  the  process  as 
was  described  for  the  other  polygons. 

By  using  the  following  figures  for  the  various  polygons,  the  miter 
lines  may  be  found ;  but  in  these  figures  no  account  is  taken  of   the 
relative  size  of  sides  to  the  foot  as  in  the  figures  preceding: 
Triangle          7   in.   and  4  in. 
Pentagon      11     "      "    8  " 
Hexagon  -      4    "      "    7 " 
Heptagon      12*  "      "    6" 


Fig.  7.    Use  of  Steel  Square  to  Find  Miter  and  Side 
ol  Octagon. 


6 


THE  STEEL  SQDARE 


Octagon        17    in.  and  7  in. 
Nonagon       22-J  "      "    9" 
Decagon         9$  "      "    3" 

The  miter  is  to  be  drawn  along  the  line  of  the  first  column,  as  shown 

for  the  triangle  in 
Fig.  8,  and  for  the 
hexagon  in  Fig.  9. 
In    Fig.     10    is 
shown    a    diagram 
for  finding  degrees 
on  the  square.   For 
example,  if  a  pitch 
of  35  degrees  is  re- 
quired, use  8gJ  on 
tongue  and   12  on 
blade;  if  45 degrees, 
12  on    tongue 
12   on  blade; 


Fig.  8.    Use  of  Square  to  Find  Miter  of  Equilateral  Triangle. 


use 
and 
etc. 


In  Fig.  11  is  shown  the  relative  length  of  run  for  a  rafter  and  a 
hip,  the  rafter  being  12  inches  and  the  hip  17  inches.  The  reason,  as 
shown  in  this  diagram,  why  17  is 
taken  for  the  run  of  the  hip,  in- 
stead of  12  as  for  the  common 
rafter,  is  that  the  seats  of  the  com- 
mon rafter  and  hip  do  not  run 
parallel  with  each  other,  but  di- 
verge in  roofs  of  equal  pitch  at  an 
angle  of  45  degrees;  therefore,  17 
inches  taken  on  the  run  of  the  hip 
is  equal  to  only  12  inches  when 
taken  on  that  of  the  common 
rafter,  as  shown  by  the  dotted 
line  from  heel  to  heel  of  the  two 
squares  in  Fig.  11. 

In  Fig.  12  is  shown  how 
other  figures  on  the  square  may  be 
found  for  corners  that  deviate  from  the  45  degrees.  It  is  shown  that 


Fig.  9.    Use  of  Square  to  Find  Miter  of 
Hexagon. 


THE  STEEL  SQUARE 


for  a  pentagon,  which  makes  a  36-degree  angle  with  the  plate,  the 

figure  to  be  used 

on  the  square  for 

run  is  14^  inches; 

for    a    hexagon, 

which   makes   a 

30-degree    angle 

with    the    plate, 

the  figure  will  be 

13|  inches;  and 

for  an   octagon, 

which  makes  an 

angle  of  22£  de- 
grees   with    the 

plate,  the  figure 

to    use    on    the 

square    for    run 

of  hip  to  corre- 
spond to  the  run 

of    the  common 

rafters,  will  be  13  inches.    It  will  be  observed  that  the  height  in  each 

case  is  9  inches. 

Fig.  13  illustrates  a 
method  of  finding  the 
relative  "height  of  a  hip 
or  valley  per  foot  run  to 
that  of  the  common  raf- 
ter. The  square  is  shown 
placed  with  12  on  blade 
and  9  on  tongue  for  the 
common  rafter;  and 
shows  that  for  the  hip  the 
rise  is  only  6,6f  inches. 

The  Steel  Square  as 
Applied  in  Roof  Fram- 
ing. Roof  framing  at 
present  is  as  simple  as  it 

possibly  can  be,  so  that  any  attempt  at  a  new  method  would  be  super- 


Fig.  10.    Diagram  for  Finding  Pitches  of  Various  Degrees 
by  Means  of  the  Steel  Square. 


Fig.  11.    Square  Applied  to  Determine  Relative 
Length  of  Run  for  Rafter  and  Hip. 


8 


THE  STEEL  SQUARE 


fluous.  There  may,  however,  be  a  certain  way  of  presenting  the  sub- 
ject that  will  carry  with  it  almost  the  weight  assigned  to  a  new  theory, 
making  what  is  already  simple  still  more  simple. 

The  steel  square  is  a  mighty  factor  in  roof  framing,  and  without 
doubt  the  greatest  tool  in  practical  potency  that  ever  was  invented 


Fig.  12.    Use  of  Square  to  Determine  Length  of  Run  for  Rafters  on  Corners 
Other  than  45°. 

for  the  carpenter.  With  its  use  the  lengths  and  bevels  of  every  piece 
of  timber  that  goes  into  the  construction  of  the  most  intricate  design 
of  roof,  can  easily  be  obtained,  and  that  with  but  very  little  knowledge 
of  lines. 

In  roofs  of  equal  pitch,  as  illustrated  in  Fig.  14,  the  steel  square 
is  all  that  is  required  if  one  properly  understands  how  to  handle  it. 


THE  STEEL  SQUARE 


What  is  meant  by  a  pitch  of  a  roof,  is  the  number  of  inches  it 
rises  to  the  foot  of  run. 

In  Fig.  15  is  shown  the  steel  square  with  figures  representing 


Fig.  13.    Method  of  Finding  Relative  Height  of  Hip  or  Valley  per  Foot  of  Run 
to  that  of  Common  Rafter. 

the  various  pitches  to  the  foot  of  run.  For  the  ^-pitch  roof,  the  figures 
as  shown,  from  12  on  tongue  to  12  on  blade,  are  those  to  be,  used  on 
the  steel  square  for  the  common  rafter;  and  for  f  pitch,  the  figures  to 
be  used  on  the  square  \vill  be  12  and  9,  as  shown. 


Fig.  14.    Diagram  to  Illustrate  Use  of  Steel  Square  in  laying  Out  Timbers 
of  Roofs  of  Equal  Pitch. 

To  understand  this  figure,  it  is  necessary  only  to  keep  in  mind 
that  the  pitch  of  a  roof  is  reckoned  from  the  span.  Since  the  run  in  each 
pitch  as  shown  is  12  inches,  the  span  is  two  times  12  inches,  which 


10 


THE  STEEL  SQUARE 


equals  24  inches;  hence,  12  on  blade  to  represent  the  foot  run,  and  12 
on  tongue  to  represent  the  rise  over  ^  the  span,  will  be  the  figures  on 
the  square  for  a  i-pitch  roof. 

For  the  f  pitch,  the  figures  are  shown  to  be  12  on  tongue  and  9 
on  blade,  9  being  f  of  the  span,  24  inches. 

The  same  rule  applies  to  all  the  pitches.  The  ^  pitch  is  shown 
to  rise  4  inches  to  the  foot  of  run,  because  4  inches  is  $  of  the  span,  24 
inches,  the  ^  pitch  is  shown  to  rise  8  inches  to  the  foot  of  run,  because 

8  inches  is  ^  of  the  span,  24  inches;  etc. 

The  roof  referred  to  in  Figs.  16  and  17  is  to 
rise  9  inches  to  the  foot  of  run;  it  is  therefore  a 
f -pitch  roof.  For  all  the  common  rafters,  the  fig- 
ures to  be  used  on  the  square  will  be  12  on  blade 
to  represent  the  run,  and  9  on  tongue  to  represent 
the  rise  to  the  foot  of  run;  and  for  all  the  hips 
and  valleys,  17  on  blade  to  represent  the  run,  and 

9  on  tongue  to  represent  the  rise  of  the  roof  to  the 
foot  of  run. 

Why  17  represents  the  run  for  all  the  hips 
and  valleys,  will  be  understood  by  examining 
Fig.  19,  in  which  17  is  shown  to  be  the  diag- 
onal of  a  foot  square. 


In  equal-pitch  roofs  the 
corners  are  square,  and  the 
plan  of  the  hip  or  valley  will 
always  be  a  diagonal  of  a 
square  corner  as  shown  at  1,  2, 
3,  and  5  in  Fig.  14. 

In  Fig.  18 
are  shown  £ 
pitch,  f  pitch 
and  ^  pitch  over 
a  square  corner. 

The  figures  to  be  used  on  the  square  for  the  hip,  will  be  17  for 
run  in  each  case.  For  the  J  pitch,  the  figures  to  l>e  used  would  be 
17  inches  run  and  4  inches  rise,  to  correspond  with  the  12  inches  run 
and  4  inches  rise  of  the  common  rafter.  For  the  -jj-  pitch,  the  figures 
to  be  used  for  hip  would  be  17  inches  run  and  9  inches  rise,  to  corre- 


I      I      I 


I- 


TIP  19   |8   17   16  15  H  13  \2   H 


2  Pitch 


Pig.  15.    Steel  Square  Giving  Various  Pitches  to  Foot  of  Run. 


THE  STEEL  SQUARE 


11 


spond  with  the  12  inches  run  and  9  inches  rise  of  the  common  rafter; 
and  for  the  £  pitch,  the  figures  to  be  used  on  the  square  will  be  17 
inches  run  and  12  inches  rise,  to  correspond  with  the  12  inches  run 
and  12  inches  rise  of  the  common  rafter. 

It  will  be  observed  from  above,  that  in  all  cases  where  the  plan 
of  the  hip  or  valley  is  a  diagonal  of  a  square,  the  figures  to  be  used  on 

Top    cut  for    I3ft.6in. 


Cut 


Rafter 


Plumb  Cut 


Fig.  16.    Method  of  Laying  Out  Common  Rafters  of  a  Ji-Pitch  Roof. 

the  square  for  run  will  be  17  inches;  and  for  the  rise,  whatever  the  roof 
rises  to  the  foot  of  run.  It  should  also  be  remembered  that  this  is  the 
condition  in  all  roofs  of  equal  pitch,  where  the  angle  of  the  hip  or 
valley  is  a  45-degree  angle,  or,  in  other  words,  where  we  have  the 
diagonal  of  a  square. 

It  has  been  shown  in  Fig.  12  how  other  figures  for  other  plan 
angles  may  be  found;  and  that  in  each  case  the  figures  for  run  vary 


Heel  cut  of  "hip 


,hip 


Top  cut  -for  laft.sm.  ruri  of 
A 


Top  cut  for  13  ft.  run  of  hip 

Fig.  17.    Method  of  Laying  Out  Hips  and  Valleys  of  a  Ji-Pitch  Roof. 

according  to  the  plan  angle  of  the  hip  or  valley,  while  the  figure  for  the 
height  in  each  ease  is  similar. 

In  Fig.  14  are  shown  a  variety  of  runs  for  common  rafters,  but 
all  have  the  same  pitch;  they  rise  9  inches  to  the  foot  of  run.  The  main 


12 


THE  STEEL  SQUARE 


roof  is  shown  to  have  a  span  of  27  feet,  which  makes  the  run  of  the 
common  rafter  13  feet  6  inches.  The  run  of  the  front  wing  is  shown 
to  be  10  feet  4  inches;  and  the  run  of  the  small  gable  at  the  left  corner 
of  the  front,  is  shown  to  be  8  feet. 

The  diversity  exhibited  in  the  runs,  and  especially  the  fractional 
part  of  a  foot  shown  in  two  of  them,  will  afford  an  opportunity  to  treat 
of  the  main  difficulties  in  laying  out  roof  timbers  in  roofs  of  equal 
pitch.  Let  it  be  determined  to  have  a  rise  of  9  inches  to  the  foot  of 

run;  and  in  this  connec- 
tion it  may  be  well  to  re- 
member that  the  propor- 
tional rise  to  the  foot  run 
for  roofs  of  equal  pitch 
makes  not  the  least  dif- 
ference in  the  method  of 
treatment. 

To  lay  out  the  common 
rafters  for  the  main  roof, 
which  has  a  run  of  13  feet 
6  inches,proceed  as  shown 
in  Fig.  16. 

Take  12  on  the  blade 
and  9  on  the  tongue,  and 
step  13  times  along  the 
rafter  timber.  This  will 
give  the  length  of  rafter 
for  13  feet  of  run.  In 
this  example,  however, 
there  is  another  6  inches 

of  run  to  cover.  For  this  additional  length,  take  6  inches  on  the  blade 
(it  being  £  a  foot  run)  for  run,  and  take  \  of  9  on  the  tongue  (which  is 
4^  inches),  and  step  one  time.  This,  in  addition  to  what  has  already 
been  found  by  stepping  13  times  with  12  and  9,  will  give  the  full  length 

of  the  rafter. 

The  square  with  12  on  blade  and  9  on  tongue  will  give  the  heel 

and  plumb  cuts. 

Another  method  of  finding  the  length  of  rafter  for  the  6  inches 
is  shown  in  Fig.  16,  where  the  square  is  shown  applied  to  the  rafter 


Fig.  18.    Method  of  Laying  Out  Hips  and  Rafters  for 
Roofs  of  Various  Pitches  over  Square  Corner. 


THE  STEEL  SQUARE  13 

timber  for  the  plumb  cut.  Square  No.  1  is  shown  applied  with  12  on 
blade  and  9  on  tongue  for  the  length  of  the  13  feet.  Square  from  this 
cut,  measure  6  inches,  the  additional  inches  in  the  run;  and  to  this 
point  move  the  square,  holding  it  on  the  side  of  the  rafter  timber 
with  12  on  blade  and  9  on  tongue,  as  for  a  full  foot  run. 

It  will  be  observed  that  this  method  is  easily  adapted  to  find  any 
fractional  part  of  a  foot  in  the  length  of  rafters. 

In  the  front  gable,  Fig.  14,  the  fractional  part  of  a  foot  is  4  inches 
to  be  added  to  10  feet  of  run;  therefore,  in  that  case,  the  line  shown 
measured  to  6  inches  in  Fig.  16  would  measure  only  4  inches  for  the 
front  gable. 

Heel  Cut  of  Common  Rafter.  In  Fig.  16  is  also  shown  a  method 
to  lay  out  the  heel  cut  of  a  common  rafter.  The  square  is  shown 
applied  with  12  on  blade  and  9  on  tongue;  and  from  where  the  12  on 
the  square  intersects  the  edge  of  the  rafter  timber,  a  line  is  drawn 
square  to  the  blade  as  shown  by  the  dotted  line  from  12  to  a.  Then 
the  thickness  of  the  part  of  the  rafter  that  is  to  project  beyond  the 
plate  to  hold  the  cornice,  is  gauged  to  intersect  the  dotted  line  at  a; 
and  from  a,  the  heel  cut  is  drawn  with  the  square  having  12  on  blade 
and  9  on  tongue,  marking  along  the  blade  for  the  cut. 

The  common  rafter  for  the  front  wing,  which  is  shown  to  have 
a  run  of  10  feet  4  inches,  is  laid  out  precisely  the  same,  except  that 
for  this  rafter  the  square  with  12  on  blade  and  9  on  tongue  will  have 
to  be  stepped  along  the  rafter  timber  only  10  times  for  the  10  feet  of 
run;  and  for  the  fractional  part  of  a  foot  (4  inches)  which  is  in  the  run, 
either  of  the  two  methods  already  shown  for  the  main  rafter  may 
be  used. 

The  proportional  figures  to  be  used  on  the  square  for  the  4  inches 
will  be  4  on  blade  and  2£  on  tongue;  and  if  the  second  method  is  used, 
make  the  addition  to  the  length  of  rafter  for  10  feet,  by  drawing  a 
line  4  inches  square  from  the  tongue  of  square  No.  1  (see  Fig.  16), 
instead  of  6  inches  as  there  shown  for  the  main  rafter. 

Hips.  Three  of  the  hips  are  shown  in  Fig.  14  to  extend  from 
the  plate  to  the  ridge-pole;  they  are  marked  in  the  figure  as  1,2,  and 
3  respectively,  and  arc  shown  in  plan  to  be  diagonals  of  a  square 
measuring  13  feet  6  inches  by  13  feet  6  inches;  they  make  an  angle, 
therefore,  of  45  degrees  with  the  plate. 


14 


THE  STEEL  SQUARE 


In  Fig.  18  it  has  been  shown  that  a  hip  standing  at  an  angle  of 
45  degrees  with  the  plate  will  have  a  run  of  17  inches  for  every  foot 
run  of  the  common  rafter.  Therefore,  to  lay  out  the  hips,  the  figures 
on  the  square  will  be  17  for  run  and  9  for  rise;  and  by  stepping  13 
times  along  the  hip  rafter  timber,  the  length  of  hip  for  13  feet  of  run 
is  obtained.  The  length  for  the  additional  6  inches  in  the  run  may 
be  found  by  squaring  a  distance  of  8^  inches,  as  shown  in  Fig.  17, 

from  the  tongue  of  the  square,  and 
moving  square  No.  1  along  the  edge 
of  the  timber,  holding  the  blade  on 
17  and  tongue  on  9,  and  marking 
the  plumb  cut  where  the  dotted  line 
is  shown. 

In  Fig.  18  is  shown  how  to  find  the 
relative  run  length  of  a  portion  of  a 
hip  to  correspond  to  that  of  a  frac- 
tional part  of  a  foot  in  the  length 
of  the  common  rafter.  From  12 
inches,  measure  along  the  run  of 
the  common  rafter  6  inches,  and 
drop  a  line  to  cut  the  diagonal  line 

in  m.  From  m  to  a,  along  the  diagonal  line,  will  be  the  relative  run 
length  of  the  part  of  hip  to  correspond  with  6  inches  run  of  the  common 
rafter,  and  it  measures  8£  inches. 

The  same  results  may  be  obtained  by  the  following  method  of 
figuring: 

As  12:17::6 

6 
12)102 

8  -  6  =  81 

In  Fig.  19  is  shown  a  12-inch  square, 
the  diagonal  m  being  17  inches.  By 
drawing  lines  from  the  base  a  &  to  cut  the 
diagonal  line,  the  part  of  the  hip  to  corre- 
spond to  that  of  the  common  rafter  will  be 
indicated  On  the  line  17.  In  this  figure 

it  is  shown  that  a  6-inch  run  on  a  b,  which  represents  the  run  of  a 
foot  of  a  common  rafter,  will  have  a  corresponding  length  of  8£ 


b 

Fig.   19.     Diagram   Showing  Relative 
Lengths  of  Run  for  Hips  and 
Common  Rafters  in  Equal- 
Pitch  Roofs. 


Fig.  20.    Method  of  Determining 

Run  of  Valley  for  Additional 

Run  in  Common  Rafter. 


THE  STEEL  SQUARE 


15 


inches  run  on  the  line  17,  which  represents  the  plan  line  of  the  hip  or 
valley  in  all  equal-pitch  roofs. 

In  the  front  gable,  Fig.  14,  it  is  shown  that  the  run  of  the  common 
rafter  is  10  feet  4  inches.    To  find  the  length  of  the  common  rafter. 


Fig.  21.    Corner  of  Square  Building,  Show-       Fig.  22.    Corner  of  Square  Building,  Show- 
ing Plan  Lines  of  Plates  and  Hip.  ing  Plan  Lines  of  Plates  and  Valley. 

take  12  on  blade  and  9  on  tongue,  and  step  10  times  along  the  rafter 
timber;  and  for  the  fractional  part  of  a  foot  (4  inches),  proceed  as  was 
shown  in  Fig.  16  for  the  rafter  of  the  main  roof;  but  in  this  case  measure 
out  square  to  the  tongue  of  square  No.  1,  4  inches  instead  of  6  inches. 
The  additional  length  for  the  fractional  4  inches  run  can  also  be 
found  by  taking  4  inches  on  blade  and  3  inches  on  tongue  of  square, 
and  stepping  one  time;  this,  in  addition  to  the  length  obtained  by 


Heel  cut  of  Valley 


Fig.  23.    Use  of  Square  to  Determine  Heel  Cut  of  Valley. 

stepping  10  times  along  the  rafter  timber  with  12  on  blade  and  9  on 
tongue,  will  give  the  full  length  of  the  rafter  for  a  run  of  10  feet  4  inches. 
In  the  intersection  of  this  roof  with  the  main  roof,  there  are  shown 
to  be  two  valleys  of  different  lengths.  The  long  one  extends  from  the 
plate  at  n  (Fig.  14)  to  the  ridge  of  the  main  roof  at  m;  it  has  therefore 


16 


THE  STEEL  SQUARE 


.Bevel  to  fit  hips 
'against  a  deep 


a  run  of  13  feet  6  inches.  For  the  length,  proceed  as  for  the  hips,  by 
taking  17  on  blade  of  the  square  and  9  on  tongue,  and  stepping  13 
times  for  the  length  of  the  13  feet;  and  for  the  fractional  6  inches, 
proceed  precisely  as  shown  in  Fig.  17  for  the  hip,  by  squaring  out  from 
the  tongue  of  square  No.  1,  8^  inches;  this,  in  addition  to  the  length 
obtained  for  the  13  feet,  will  give  the  full  length  of  the  long  valley  n  m. 
The  length  of  the  short  valley  a  c,  as  shown,  extends  over  the 
run  of  10  feet  4  inches,  and  butts  against  the  side  of  the  long  valley  at  c. 
By  taking  17  on  blade  and  9  on  tongue,  and  stepping  along  the  rafter 
timber  10  times,  the  length  for  the  10  feet  is  found;  and  for  the  4 

inches,  measure  5| 
inches  square  from 
the  tongue  of 
square  No.  1,  in 
the  manner  shown 
in  Fig.  17,  where 
the  8£  inches  is 
added  for 
the  6  inches  addi- 
tional run  of  the 
main  roof  for  the 
hips. 

The  length  5f  is 
found  as  shown  in 
Fig.  20,  by  meas- 
uring 4  inches  from 
atom  along  the  run 

of  common  rafter  for  one  foot.  Upon  m  erect  a  line  to  cut  the  seat  of 
the  valley  at  c;  from  c  to  a  will  be  the  run  of  the  valley  to  correspond 
with  4  inches  run  of  the  common  rafter,  and  it  will  measure  5g  inches. 
How  to  Treat  the  Heel  Cut  of  Hips  and  Valleys.  Having  found 
the  lengths  of  the  hips  and  valleys  to  correspond  to  the  common  rafters, 
it  will  be  necessary  to  find  also  the  thickness  of  each  above  the  plate 
to  correspond  to  the  thickness  the  common  rafter  will  be  above  the 
plate. 

In  Fig.  21  is  shown  a  corner  of  a  square  building,  showing  the 
plates  and  the  plan  lines  of  a  hip.  The  length  of  the  hip,  as  already 
found,  will  cover  the  span  from  the  ridge  to  the  corner  2;  but  the  sides 


Fig.  34.    Steel  Square  Applied  to  Finding  Bevel  for  Fitting 
Top  of  Hip  or  Valley  to  Ridge. 


THE  STEEL  SQUARE 


17 


of  the  hip  intersect  the  plates  at  3  and  3  respectively;  therefore  the 
distance  from  2  to  1,  as  shown  in  this  diagram,  is  measured  backwards 
from  a  to  1  in  the  manner  shown  in  Fig.  17;  then  a  plumb  line  is  drawn 
through  1  to  ra,  parallel  to  the  plumb  cut  a-17.  From  ra  to  o  on  this 
line,  measure  the  same  thickness  as  that  of  the  common  rafter;  and 
through  o  draw  the  heel  cut  to  a  as  shown. 

In  like  manner  the  thickness  of  the  valley  above  the  plate  is  found ; 
but  as  the  valley  as  shown  in  the  plan  figure,  Fig.  22,  projects  beyond 
point  2  before  it  intersects  the  outside  of  the  plates,  the  distance  from 
2  to  1  in  the  case  of  the  valley  will  have  to  be  measured  outwards  from 
2,  as  shown  from 
2tol  in  Fig.  23; 
and  at  the  point 
thus  found  the 
thickness  of  the 
valley  is  to  be 
measured  to  cor- 
respond  with 
that  of  the  com- 
mon rafter  as 
shown  at  ra  n. 

In  Fig.  24  is 
shown  the  steel 
square  applied  to 
a  hip  or  valley 
timber  to  cut  the 
bevel  that  will 

fit  the  top  end  against  the  ridge.  The  figures  on  the  square  are  17 
and  19 J.  The  17  represents  the  length  of  the  plan  line  of  the  hip 
or  valley  for  a  foot  of  run,  which,  as  was  shown  in  previous  figures, 
will  always  be  17  inches  in  roofs  of  equal  pitch,  where  the  plan  lines 
stand  at  45  degrees  to  the  plates  and  square  to  each  other. 

The  19}  taken  on  the  blade  represents  the  actual  length  of  a  hip 
or  valley  that  will  span  over  a  run  of  17  inches.  The  bevel  is  marked 
along  the  blade. 

The  cut  across  the  back  of  the  short  valley  to  fit  it  against  the 
side  of  the  long  valley,  will  be  a  square  cut  owing  to  the  two  plan  lines 
being  at  right  angles  to  each  other. 


X-  Bevel  to  fit  bacK 
'    of  jacks  against 
hip  or  valley 


Fig.  25.    Steel  Square  Applied  to  Jack  Rafter  to  Find  Bevel  for 
Fitting  against  Side  or  Hip  or  Valley. 


18  THE  STEEL  SQUARE 

In  Fig.  25  is  shown  the  steel  square  applied  to  a  jack  rafter  to 
cut  the  back  bevel,  to  fit  it  against  the  side  of  a  hip  or  valley.  The 
figures  on  the  square  are  12  on  tongue  and  15  on  blade,  the  12  repre- 
senting a  foot  run  of  a  common  rafter,  and  the  15  the  length  of  a 
rafter  that  will  span  over  a  foot  run;  marking  along  the 
blade  will  give  the  bevel. 

The  rule  in  every  case  to  find  the  back  bevel  for  jacks  in 
roofs  of  equal  pitch,  is  to  take  12  on  the  tongue  to  represent 
the  foot  run,  and  the  length  of  the  rafter  for  a  foot  of  run  on 
the  blade,  marking  along  the  blade  in  each  case  for  the 
bevel. 

In  a  ^-pitch  roof,  which  is  the 
most  common   in  all   parts  of  the 


country,  the  length  of  rafter  for  a    H  I  I  I  I  ixfi  I  I  I  I  I  1  I  I  I 
foot  of  run  will  be  17  inches;  hence  '2     Run  of  Rafter 

Fig.  26.-  Finding  Length  to  Shorten 

it  will  be  well  to  remember  that  12  Raftersfor^  .racks  per  Foot 

on  tongue  and  17  on  blade,  marking 

along  the  blade,  will  give  the  bevel  to  fit  a  jack  against  a  hip  or  a 
valley  in  a  |-pitch  roof. 

In  a  roof  having  a  rise  of  9  inches  to  the  foot  of  run,  such  as  the 
one  under  consideration,  the  length  of  rafter  for  one  foot  of  run  will 
be  15  inches.  The  square  as  shown  in  Fig.  25,  with  12  on  tongue  and 
15  on  blade,  will  give  the  bevel  by  marking  along  the  blade. 

To  find  the  length  of  a  rafter  for  a  foot  of  run  for  any  other  pitch, 
place  the  two-foot  rule  diagonally  from  12  on  the  blade  of  the  square 
to  the  figure  on  tongue  representing  the  rise  of  the  roof  to  the  foot  of 
run;  the  rule  will  give  the  length  of  the 
rafter  that  will  span  over  one  foot  of 
run. 

The  length  of  rafter  for  a  foot  of 
run  will  also  determine  the  difference 
in  lengths  of  jacks.  For  example,  if  a 
roof  rises  12  inches  to  one  foot  of  run, 

Fig.  27.    Finding  Length  of  Jack  ,  „  ,  .  i        i  j-          i 

Rafter  in  ^-Pitch  Roof.  the  rafter  over  this  span  has  been  found 

to  be  17  inches;  this,  therefore,  is  the 

number  of  inches  each  jack  is  shortened  in  one  foot  of  run.  If  the 
rise  of  the  roof  is  8  inches  to  the  foot  of  run,  the  length  of  the  rafter  is 
found  for  one  foot  of  run,  by  placing  the  rule  diagonally  from  12  on 


THE  STEEL  SQUARE 


19 


tongue  to  8  on  blade,  which  gives  14 \  inches,  as  shown  in  Fig.  26. 
This,  therefore,  will  be  the  number  of  inches  the  jacks  are  to  be 
shortened  in  a  roof  rising  8  inches  to  the  foot  of  run.  If  the  jacks  are 
placed  24  inches  from  center  to  center,  then  multiply  14£  by  2  =  29 
inches. 

In  Fig.  27  is  shown  how  to  find 
the  length  with  the  steel  square.  The 
square  is  placed  on  the  jack  timber 
rafter  with  the  figures  that  have  been 
used  to  cut  the  common  rafter.  In 
Fig.  27,  12  on  blade  and  12  on  tongue 
were  the  figures  used  to  cut  the  com- 
mon rafter,  the  roof  being  \  pitch, 

rising  12  inches  to  the  foot  of  run.  In  the  diagram  it  is  shown  how 
to  find  the  length  of  a  jack  rafter  if  placed  16  inches  from  center  to 
center.  The  method  is  to  move  the  square  as  shown  along  the  line  of 
the  blade  until  the  blade  measures  16  inches;  the  tongue  then  would  be 
as  shown  from  w  to  m,  and  the  length  of  the  jack  would  be  from  12  on 
blade  to  m  on  tongue,  on  the  edge  of  the  jack  rafter  timber  as  shown. 

This  latter  method  becomes  convenient  when  the  space  between 
jacks  is  less  than  18  inches;  but  if  used  when  the  space  is  more  than 


Fig.  28.    Finding  Length  of  Jack 
Rafter  in  ^-Pitch  Roof . 


Fig.  29. 


Method  of  Determining  Length  of  Jacks  Between  Hips  and  Valleys; 
also  Bevels  for  Jacks,  Hips,  and  Valleys. 


18  inches  it  will  become  necessary  to  use  two  squares;  otherwise  the 
tongue  as  shown  at  m  would  not  reach  the  edge  of  the  timber. 

In  Fig.  28  the  same  method  is  shown  for  finding  the  length  of  a 
jack  rafter  for  a  roof  rising  9  inches  to  the  foot  of  run,  with  the  jacks 
placed  18  inches  center  to  center.  The  square  in  this  diagram  is 
shown  placed  on  the  jack  rafter  timber  with  12  on  blade  and  9  on 


20 


THE  STEEL  SQUARE 


tongue;  then  it  is  moved  forward  along  the  line  of  the  blade  to  w. 
The  blade,  when  in  this  latter  position,  will  measure  18  inches.  The 
tongue  will  meet  the  edge  of  the  timber  at  m,  and  the  distance  from 
m  on  tongue  to  12  on  blade  will  indicate  the  length  of  a  jack,  or,  in 
other  words,  will  show  the  length  each  jack  is  shortened"  when  placed 


Miter  Bevel  for  Boards 


Bevel   to  cut 


Pig.  30.    Method  of  Finding  Bevels  for  All  Timbers  in  Roofs  of  Equal  Pitch. 

18  inches  between  centers  in  a  roof  having  a  pitch  of  9  inches  to  the 
foot  of  run. 

When  jacks  are  placed  between  hips  and  valleys  as  shown  at 
1,  2,  3,  4,  etc.,  in  Fig.  14,  a  better  method  of  treatment  is  shown  in 
Fig.  29,  where  the  slope  of  the  roof  is  projected  into  the  horizontal 
plane.  The  distance  from  the  plate  in  this  figure  to  the  ridge  m,  equals 
the  length  of  the  common  rafter  for  the  main  roof.  On  the  plate  ann 
is  made  equal  to  a  n  n  in  Fig.  14.  By  drawing  a  figure  like  this  to  a 
scale  of  one  inch  to  one  foot,  the  length  of  all  the  jacks  can  be  measured 


THE  STEEL  SQUARE  21 

and  also  the  lengths  of  the  hip  and  the  two  valleys.  It  also  gives  the 
bevels  for  the  jacks,  as  well  as  the  bevel  to  fit  the  hip  and  valley  against 
the  ridge;  but  this  last  bevel  must  be  applied  to  the  hip  and  valley 
when  backed. 

It  has  been  shown  before,  that  the  figures  to  be  used  on  the 
square  for  this  bevel  when  the  timber  is  left  square  on  back  as  is  the 
custom  in  construction,  are  the 
length  of  a  foot  run  of  a  hip  or  val- 
ley,  which  is  17,  on  tongue,  and  the 
length  of  a  hip  or  valley  that  will 
span  over  17  inches  run,  on  blade — 
the  blade  giving  the  bevel. 

Fig.  31.    Method  of  Finding  Bevel  5,  Fig. 

Flff.  30  Contains  all  the  bevels  or       «>,  for  Fitting  Hip  or  Valley  Against 

Ridge  when  not  Backed. 

cuts  that  have  been  treated  upon  so 

far,  and,  if  correctly  understood,  will  enable  any  one  to  frame  any 
roof  of  equal  pitch.  In  this  figure  it  is  shown  that  12  inches  run  and 
9  inches  rise  will  give  bevels  1  and  2,  which  are  the  plumb  and  heel 
cuts  of  rafters  of  a  roof  rising  9  inches  to  the  foot  of  run.  By  taking 
these  figures,  therefore,  on  the  square,  9  inches  on  the  tongue  and  12 
inches  on  the  blade,  marking  along  the  tongue  will  give  the  plumb  cut, 
and  marking  along  the  blade  will  give  the  heel  cut. 

Bevels  3  and  4  are  the  plumb  and  heel  cuts  for  the  hip,  and  are 
shown  to  have  the  length  of  the  seat  of  hip  for  one  foot  run,  which  is 
17  inches.  By  taking  17  inches,  therefore,  on  the  blade,  and  9  inches 
on  the  tongue,  marking  along  the  tongue  for  the  plumb  cut,  and  along 

Miter  cut  for  roo<  board 


Fig.  32.    Method  of  Finding  Back  Bevel  6,          Fig.  33.    Determining  Miter  Cut  for  Roof- 
Fig.  30,  for  Jack  Rafters,  and  Bevel  Board. 
7,  for  Roof -Board. 

the  blade  for  the  heel  cut,  the  plumb  and  heel  cuts  are  found.  Bevel 
5,  which  is  to  fit  the  hip  or  valley  against  the  ridge  when  not  backed, 
is  shown  from  o  w,  the  length  of  the  hip  for  one  foot  of  run,  which  is 
19J  inches,  and  from  o  s,  which  always  in  roofs  of  equal  pitch  will 
be  17  inches  and  equal  in  length  to  the  seat  of  a  hip  or  valley  for  one 
foot  of  run. 


22 


THE  STEEL  SQUARE 


These  figures,  therefore,  taken  on  the  square,  19£  on  the  blade, 

and  17  on  the  tongue,  will  give  the  bevel  by  marking  along  the  blade 

as  shown  in  Fig.  31,  where  the  square  is  shown  applied  to  the  hip 

timber  with  19£  on  blade  and  17  on  tongue, 

the  blade  showing  the  cut. 

Bevels  6  and  7  in  Fig.  30  are  shown 

formed  of  the  length  of  the  rafter  for  one  foot 

of  run,  which  is  15  inches,  and  the  run  of  the 

rafter,  which  is  12  inches.    These  figures  are 

applied    on    the 

square,  as  shown 

in  Fig.  32,  to  a 

jack  rafter  tim- 
ber; taking  15  on 

the  blade  and  12 

on    the    tongue, 

marking  along 

the  blade  will 

give  the  back  bevel  for  the  jack  rafters,  and  marking  along  the  tongue 

will  give  the  face  cut  of  roof -boards  to  fit  along  the  hip  or  valley. 
It  is  shown  in  Fig.  30,  also,  that  by  taking  the  length  of  rafter 

15  inches  on  blade,  and  rise  of  roof  9  inches  on  tongue,  bevel  8  will 

give  the  miter  cut  for  the  root-boards. 

In  Fig.  33  the  square  is  shown  applied  to  a  roof-board  with  15 

on  blade,  which  is  the  length  of  the  rafter  to  one  foot  of  run,  and 

with  9  on  tongue,  which  is  the  rise  of  the  roof  to  the  foot  run;  marking 

along  the  tongue  will  give  the  miter  for  the  boards. 

Other  uses  may  be  made  of  these 
figures,  as  shown  in  Fig.  34,  which 
is  one-half  of  a  gable  of  a  roof  ris- 
ing 9  inches  to  the  foot  run.  The 
squares  at  the  bottom  and  the  top 
will  give  the  plumb  and  heel  cuts  of 
the  common  rafter.  The  same 


Fig.  34.     Laying  Out  Timbers  of  One-half  Gable  of  Ji-Pitch  Roof. 


of   hip 


Fig.  35.    Finding  Backing  of  Hip  in 


figures  on  the  square  applied  to  the  studding,  marking  along  the 
tongue  for  the  cut,  will  give  the  bevel  to  fit  the  studding  against  the 
rafter;  and  by  marking  along  the  blade  we  obtain  the  cut  for  the 
boards  that  run  across  the  gable.  By  taking  19£  on  blade,  which  is 


THE  STEEL  SQUARE 


23 


the  length  of  the  hip  for  one  foot  of  run,  and  taking  on  the  tongue  the 
rise  of  the  roof  to  the  foot  of  run,  which  is  9  inches,  and  applying 
these  as  shown  in  Fig.  35,  we  obtain  the  backing  of  the  hip  by 
marking  along  the  tongue  of  the  two  squares,  as  shown. 

It  will  be  observed  from  what  has  been  said,  that  in  roofs  of 
equal  pitch  the  figure  12  on  the  blade,  and  whatever  number  of  inches 
the  roof  rises  to  the  foot  run  on  the  tongue,  will  give  the  plumb  and 
heel  cuts  for  the  common  rafter;  and  that  by  taking  'Jl  on  the  blade 
instead  of  12,  and  taking  on  the  tongue  the  figure  representing  the 
rise  of  the  roof  to  the  foot  run,  the  plumb  and  heel  cuts  are  found  for 
the  hips  and  valleys. 

By  taking  the  length  of  the  common  rafter  for  one  foot  of  run 
on  blade,  and  the  run  12  on  tongue,  marking  along  the  blade  will  give 


6  6 

Fig.  36.    Laying  Out  Timbers  of  Roof  with  Two  Unequal  Pitches. 


the  back  bevel  for  the  jack  to  fit  the  hip  or  valley,  and  marking  along 
the  tongue  will  give  the  bevel  to  cut  the  roof-boards  to  fit  the  line  of 
hip  or  valley  upon  the  roof. 

With  this  knowledge  of  what  figures  to  use,  and  why  they  are 
used,  it  will  be  an  easy  matter  for  anyone  to  lay  out  all  rafters  for 
equal-pitch  roofs. 

In  Fig.  36  is  shown  a  plan  of  a  roof  with  two  unequal  pitches. 
The  main  roof  is  shown  to  have  a  rise  of  12  inches  to  the  foot  run.  The 
front  wing  is  shown  to  have  a  run  of  6  feet  and  to  rise  12  feet;  it  has 
thus  a  pitch  of  24  inches  to  the  foot  run.  Therefore  12  on  blade  of  the 
square  and  12  on  tongue  will  give  the  plumb  and  heel  cuts  for  the 
main  roof,  and  by  stepping  12  times  along  the  rafter  timber  the  length 
of  the  rafter  is  found.  The  figures  on  the  square  to  find  the  heel  and 


24 


THE  STEEL  SQUARE 


plumb  cuts  for  the  rafter  in  the  front  wing,  will  be  12  run  and  24  rise, 
and  by  stepping  6  times  (the  number  of  feet  in  the  run  of  the  rafter), 
the  length  will  be  found  over  the  run  of  6  feet,  and  it  will  measure  13 
feet  6  inches. 

If,  in  place  of  stepping  along  the  timber,  the  diagonal  of  12  and 
24  is  multiplied  by  6,  the  number  of  feet  in  the  run, 
the  length  may  be  found  even  to  a  greater  exactitude. 

Many  carpenters  use  this  method  of  framing;  and 
to  those  who  have  confidence  in  their  ability  to  figure 
correctly,  it  is  a  saving  of  time,  and,  as  before  said, 
will  result  in  a  more  accurate  measurement;  but  the 
better  and  more  scientific  method  of  framing  is  to  work 
to  a  scale  of  one  inch,  as  has  already  been  explained. 

According  to  that  method,  the 
diagonal  of  a  foot  of  run,  and  the 
number  of  inches  to  the  foot  run  the 
roof  is  rising,  measured  to  a  scale, 
will  give  the  exact  length.  For 
example,  the  main  roof  in  Fig.  36  is 
rising  12  inches  to  a  foot  of  run.  The  diagonal  of  12  and  12  is  1 7 
inches,  which,  considered  as  a  scale  of  one  inch  to  a  foot,  will  give 

(Ridqe 


Fig.  37.    Finding  Length  of  Rafter  for 
Front  Wing  in  Roof  Shown  in 

Fig.  36. 


Fig.  38.    Laying  Out  Timbers  of  Roof  Shown  in  Fig.  36,  by  Projecting  Slope  of 
Roof  into  Horizontal  Plane. 

17  feet,  and  this  will  be  the  exact  length  of  the  rafter  for  a  roof  rising 
12  inches  to  the  foot  run  and  having  a  run  of  12  feet. 

The  length  of  the  rafter  for  the  front  wing,  which  has  a  run  of  6 
feet  and  a  rise  of  12  feet,  may  be  obtained  by  placing  the  rule  as  shown 


THE  STEEL  SQUARE 


Elevation 


in  Fig.  37  from  6  on  blade  to  12  on  tongue,  which  will  give  a  length  of 
13}  inches.  Jf  the  scale  be  considered  as  one  inch  to  a  foot,  this  will 
equal  13  feet  6  inches,  which  will  be  the  exact  length  of  a  common 
rafter  rising  24  inches  to  the  foot  run  and  having  a  run  of  6  feet. 

It  will  be  observed  that  the  plan  lines  of  the  valleys  in  this  figure 
in  respect  to  one  another  deviate  from  forming  a  right  angle.  In 
equal-pitch  roofs  the  plan  lines  are  always  at  right  angles  to  each  other, 
and  therefore  the  diagonal  of  12  and  12,  which  is  17  inches,  will  be 
the  relative  foot  run  of  valleys  and  hips  in  equal-pitch  roofs. 

In  Fig.  36  is  shown  how  to  find  the  figures  to  use  on  the  square 
for  valleys  and  hips  when  deviating 
from  the  right  angle.  A  line  is 
drawn  at  a  distance  of  12  inches 
from  the  plate  and  parallel  to  it, 
cutting  the  valley  in  ra  as  shown. 
The  part  of  the  valley  from  ra  to 
the  plate  will  measure  13£  inches, 
which  is  the  figure  that  is  to  be 
used  on  tli3  square  to  obtain  the 
length  and  cuts  of  the  valleys. 

It  will  be  observed  that  this 
equals  the  length  of  the  common 
rafter  as  found  by  the  square  and 
rule  in  Fig.  37.  In  that  figure  is 
shown  12  on  tongue  and  6  on  blade. 
The  12  here  represents  the  rise,  and 
the  6  the  run  of  the  front  roof.  If 
the  12  be  taken  to  represent  the 
run  of  the  main  roof,  and  the  6  to 
represent  the  run  of  the  front  roof,  then,  the  diagonal  13\  will  indi- 
cate the  length  of  the  seat  of  the  valley  for  12  feet  of  run,  and  there- 
fore for  one  foot  it  will  be  13\  inches.  Now,  by  taking  13\  on  the 
blade  for  run,  and  12  inches  on  the  tongue  for  rise,  and  stepping 
along  the  valley  rafter  timber  12  times,  the  length  of  the  valley 
will  be  found.  The  blade  will  give  the  heel  cut,  and  the  tongue  the 
plmnb  cut. 

In  Fig.  38  is  shown  the  slope  of  the  roof  projected  into  the  hori- 
zontal plane.  By  drawing  a  figure  based  on  a  scale  of  one  inch  to  one 


Plan 


Fig.  39.  Method  of  Finding  Length  and 
Cuts  of  Octagon  Hips  Intersect- 
ing a  Roof. 


THE  STEEL  SQUARE 


foot,  all  the  timbers  on  the  slope  of  the  roof  can  be  measured.  Bevel 
2,  shown  in  this  figure,  is  to  fit  the  valleys  against  the  ridge.  By 
drawing  a  line  from  w  square  to  the  seat  of  the  valley  to  m,  making 


~  -^  .Ridqe  in  Second  Position 


Fig.  40.    Showing  How  Cornice  Aflects  Valleys  and  Plates  in  Roof  with  Unequal  Pitches. 

w  2  equal  in  length  to  the  length  of  the  valley,  as  shown,  and  by  con- 
necting 2  and  m,  the  bevel  at  2  is  found,  which  will  fit  the  valleys 
against  the  ridge,  as  shown  at  3  and  3  in  Fig.  36. 

In  Fig.  39,  is  shown  how  to  find  the  length  and  cuts  of  octagon 
hips  intersecting  a  roof.  In  Fig.  36,  half  the  plan  of  the  octagon  is 
shown  to  be  inside  of  the  plate,  and  the  hips  o,  z,  o  intersect  the  slope 
of  the  roof.  In  Fig.  39,  the  lines  below  x  y  are  the  plan  lines ;  and  those 

above,  the  elevation.  From  z,  o: 
o,  in  the  plan,  draw  lines  to  x  y, 
as  shown  from  o  to  m  and  from  z 
to  m;  from  m  and  m,  draw  the  ele- 
vation lines  to  the  apex  o",  inter- 
secting the  line  of  the  roof  in  d" 
and  c".  From  d"  and  c",  draw 
the  lines  d"  v"  and  c"  a"  parallel 
to  x  y\  from  c",  drop  a  line  to  in- 
tersect the  plan  line  a  o  in  c. 
Make  a  w  equal  in  length  to  a"  o" 
of  the  elevation,  and  connect  w  c; 

Fig.  41.    Showing  Relative  Position  of  . 

Plates  in  Roof  with  TWO  un-  measure  irom  w  to  n  the  lull  height 

equal  Pitches. 

of  the  octagon  as  shown  from  xy 
to  the  apex  o";  and  connect  c  n.    The  length  from  w  to  c  is  that  of 


THE  STEEL  SQUARE 


127 


Seat  of  Valley 
/        ^       .<;      / 


^x 

\ 

S 

3 

x 

v 

\ 

S 

Purl  rr» 

, 

2 

m          j 

^  Plate 

V 

the  two  hips  shown  at  o  o  in  Fig.  36,  both  being  equal  hips  intersect- 
ing the  roof  at  an  equal  distance  from  the  plate.  The  bevel  at  w  is  the 
top  bevel,  and  the  bevel  at  c  will  fit  the  roof. 

Again,  drop  a  line  from  d"  to  intersect  the  plan  line  az'md. 
Make  a  2  equal  to  if  o"  in  the  elevation,  and  connect  2  d.  Measure 
from  2  to  b  the  full  height  of  the  tower  as  shown  from  x  y  to  the  apex 
o"  in  the  elevation,  and  connect  d  b. 
The  length  2  d  represents  the 
length  of  the  hip  z  shown  in 
Fig.  36;  the  bevel  at  2  is  that  of 
the  top;  and  the  bevel  aid,  the 
one  that  will  fit  the  foot  of  the 
hip  to  the  intersecting  roof. 

When  a  cornice  of  any  con- 
siderable width  runs  around  a 
roof  of  this  kind,  it  affects  the 
plates  and  the  angle  of  the  val- 
leys as  shown  in  Fig.  40.  In 
this  figure  are  shown  the  same 
valleys  as  in  Fig.  36;  but,  owing 
to  the  width  of  the  cornice,  the 
foot  of  each  has  been  moved  the 
distance  a  b  along  the  plate  of  the 
main  roof.  Why  this  is  done  is 

shown  in  the  drawing  to  be  caused  by  the  necessity  for  the  valleys 
to  intersect  the  corners  c  c  of  the  cornice. 

The  plates  are  also  affected  as  shown  in  Fig.  41,  where  the  plate 
of  the  narrow  roof  is  shown  to  be  much  higher  than  the  plate  of  the 
main  roof. 

The  bevels  shown  at  3,  Fig.  40,  are  to  fit  the  valleys  against  the 
ridge. 

In  Fig.  42  is  shown  a  very  simple  method  of  finding  the  bevels  for 
purlins  in  equal-pitch  roofs.  Draw  the  plan  of  the  corner  as  shown, 
and  a  line  from  m  to  o;  measure  from  o  the  length  x  y,  representing 
the  common  rafter,  to  w;  from  w  draw  a  line  to  m;  the  bevel  shown 
at  2  will  fit  the  top  face  of  the  purlin.  Again,  from  o,  describe  an 
arc  to  cut  the  seat  of  the  valley,  and  continue  same  around  to  S;  con- 
nect S  m;  the  bevel  at  3  will  be  the  side  bevel. 


i/ 
x 

Fig.  42.    Method  of  Find  ing  Bevels  for  Pur- 
lins in  Equal-Pitch  Roofs. 


INDEX. 


INDEX 


PART  PAGE 

B 

Hcvel -  I,  44 

Bevels,  application  of  in  fit  ting  wreaths  to  rail 1 ,  58 

Hevels  to  square  wreaths I,  60 

Bottom  steps  with  obtuse-angle  plan I,  56 

Bullnose  stair I,  33 

Bullnose  steps. I,  32 

Bullnose  tread I,  '  29 

C 

Carriage I,  16 

Carriage  pieces I,  28 

Circular  stairs I,  25 

Close  stairway I,  2 

Cove I,  28 

Curved  steps  and  stringer,  plan  of I,  54 

Cylinder I,  35 

D 

Dog-legged  stairs I,  25 

F 

Face-mould I,  68 

Face-mould  developing  (obtuse-angle  plan) I,  56 

Flyer I,  25 

Foci I,  70 

G 

Geometrical  stair I,  44 

Geometrical  stairways  and  handrailing I,  43 

K 

Kerfing I,  36 

N 

Newel  post I,  14 

O 

Open-newel  stairs I,  32 

P 

Pitch-board I,  10 

Plan  lines .  I,  48 

Platform I,  20 

Platform  stairs I,  26 

Projection I,  44 


2  INDEX 

PART       PAGE 

Q 

Quarter-space  stair  with  six  winders I,       43 

Quick  sweep I,       37 

R 

Rail,  plan  line  of I,  46 

Rise  and  rim I,  3 

Riser I,  3 

arrangement  of I,  74 

Rough  brackets 


S 

Spriaging  the  plank I,  74 

Stair  with  five  dancing  winders I,  43 

Stair-building I,  1-75 

definitions . I,  2 

introductory I,  1 

laying  out I,  22 

open-newel  stairs I,  32 

platform _ I,  20 

stairs  with  curved  turns I,  34 

strings _.    I,  7 

housed.. I,  7 

notched I,  8 

open I,  7 

rough I,  7 

staved I,  8 

well  hole . I,  18 

Stairs,  plans  and  elevation  turning  around  central  post I,  44 

Stairs,  setting  of I,  8 

Stairs,  types  of  in  common  use I,  41 

Steel  square II,  1-27 

applied  in  roof  framing II,  7 

applied  to  jack  rafter II,  17 

back II,  1 

back  of  blade,  showing  essex  board  measure II,  3 

back  of  blade,  showing  rafter  table II,  2 

back  of  tongue,  showing  brace  measure II,  3 

bevels,  method  of  finding  for  all  timbers  in  roofs  of  equal  pitch II,  20 

blade II,  1 

board  measure II,  I 

brace  rule II,  1 

common  rafters,  method  of  laying  out II,  11 

face . II,  1 

face  side  of  tongue,  showing  octagon  scale II,  2 

finding  backing  of  hip  in  gable  roof II,  22 

finding  length  of  rafter  for  front  wing  in  roof  shown  in  Fig.  36 II,  24 

finding  length  to  shorten  rafters  for  jacks  per  foot  of  run  —        -  -  II,  18 

giving  various  pitches  to  foot  of  run II,  10 


INDEX  3 

PART  PAOB 

Steel  square  (continued) 

heel  cut  of  common  rafter II,  13 

hips...               ...II,  13 

hips  and  rafters  for  roofs  of  various  pitches  over  square  corner, 

method  of  laying  out II,  12 

hips  and  valleys,  how  to  treat  the  heel  cut  of II,  16 

hips  and  valleys  of  a  f-pitch  roof,  method  of  laying  out .II,  11 

jack  rafter,  finding  length  of II,  18 

jacks  between  hips  and  valleys,  method  of  determining  length II,  19 

laying  out  timbers  of  one-half  gable  of  f-pitch  roof II,  22 

laying  out  timbers  of  roof  with  two  unequal  pitches II,  23 

method  of  finding  bevels  for  purlins  in  equal-pitch  roofs II,  27 

method  of  finding  length  and  cuts  of  octagon  hips  intersecting  a 

roof . II,  25 

octagon  scale II,  1 

rise  and  run II,  1 

tongue II,  1 

use  of  to  find  miter  of  equilateral  triangle II,  6 

use  of  to  find  miter  of  hexagon II,  6 

use  of  to  find  miter  and  side  of  pentagon,  hexagon  and  octagon. . .    I,  4,  5 

Story  rod .-    I,  8 

Straight  flights I,  25 

String-board I,  3 

Strings I,  7 

housed I,  7 

methods  of  building  up I,  37 

notched I,  8 

open I,  7 

rough I,  7 

staved I,  8 

T 

Tangent  inclined-lower  tangent  level I,  63 

Tangent  system I,  44 

Tangents  and  face-mould,  diagram  of I,  53 

Tangents  unfolded I,  50 

Tread I,  3 

Treads  and  risers,  housing  of I,  13 

Trimming  joists I,  19 

Twisted  wreath  raised  to  position I,  57 

W 

Well-hole I,  18 

Well-hole  connecting  two  flights I,  51 

Winder I,  25 

Winding  stairs I,  25 

Wreath,  cut  ting  from  plank I,  57 

Wreath  with  two  equally  inclined  tangents,  finding  bevels  for I,  59 

Wreath  twisted,  ready  to  be  moulded I,  57 

Wreaths. I,  43 


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